Prévost, Alexis First passage percolation, local uniqueness for interlacements and capacity of random walk. (English) Zbl 07966802 Commun. Math. Phys. 406, No. 2, Paper No. 34, 75 p. (2025). MSC: 60K35 60G50 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Mu, Yingxin; Sapozhnikov, Artem On questions of uniqueness for the vacant set of Wiener sausages and Brownian interlacements. (English) Zbl 07938774 Probab. Theory Relat. Fields 190, No. 3-4, 703-751 (2024). MSC: 60K35 60J65 60G55 82B43 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Drewitz, A.; Elias, O.; Prévost, A.; Tykesson, J.; Viklund, F. Percolation for two-dimensional excursion clouds and the discrete Gaussian free field. (English) Zbl 1546.60178 Electron. J. Probab. 29, Paper No. 118, 54 p. (2024). MSC: 60K35 60J65 60G15 60G60 60J67 82B43 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Duminil-Copin, Hugo; Goswami, Subhajit; Rodriguez, Pierre-François; Severo, Franco; Teixeira, Augusto A characterization of strong percolation via disconnection. (English) Zbl 07900378 Proc. Lond. Math. Soc. (3) 129, No. 2, Article ID e12622, 49 p. (2024). MSC: 60K35 82B43 60G50 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Han, X.; Zhang, Y.; Ge, H. Cover-time Gumbel fluctuations in finite-range, symmetric, irreducible random walks on torus. (English) Zbl 1541.60032 J. Phys. A, Math. Theor. 57, No. 28, Article ID 285203, 17 p. (2024). MSC: 60G50 60J10 60K35 05C81 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Li, Xinyi; Zhuang, Zijie On large deviations and intersection of random interlacements. (English) Zbl 07874413 Bernoulli 30, No. 3, 2102-2126 (2024). MSC: 60K35 60F10 60G50 × Cite Format Result Cite Review PDF Full Text: DOI arXiv Link
Dickson, Matthew; Vogel, Quirin Formation of infinite loops for an interacting bosonic loop soup. (English) Zbl 1534.60141 Electron. J. Probab. 29, Paper No. 24, 39 p. (2024). MSC: 60K35 60F10 60J65 60G50 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Collin, Orphée; Popov, Serguei Two-dimensional random interlacements: 0-1 law and the vacant set at criticality. (English) Zbl 1534.60139 Stochastic Processes Appl. 169, Article ID 104272, 8 p. (2024). MSC: 60K35 60G50 60J65 82C41 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Vogel, Quirin Emergence of interlacements from the finite volume Bose soup. (English) Zbl 1533.60183 Stochastic Processes Appl. 166, Article ID 104227, 43 p. (2023). MSC: 60K35 60G55 82B41 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Mu, Yingxin; Sapozhnikov, Artem Uniqueness of the infinite connected component for the vacant set of random interlacements on amenable transient graphs. (English) Zbl 1546.60186 Electron. Commun. Probab. 28, Paper No. 55, 9 p. (2023). MSC: 60K35 82C41 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Sznitman, Alain-Sol On bulk deviations for the local behavior of random interlacements. (Sur les déviations massives du comportement local des entrelacs aléatoires.) (English. French summary) Zbl 1531.60028 Ann. Sci. Éc. Norm. Supér. (4) 56, No. 3, 801-858 (2023). Reviewer: Oleg K. Zakusilo (Kyïv) MSC: 60F10 60K35 60J55 82B43 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Borbényi, Márton; Ráth, Balázs; Rokob, Sándor Random interlacement is a factor of i.i.d. (English) Zbl 1528.60093 Electron. J. Probab. 28, Paper No. 58, 45 p. (2023). MSC: 60K35 82B20 × Cite Format Result Cite Review PDF Full Text: DOI arXiv Link
Prévost, Alexis Percolation for the Gaussian free field on the cable system: counterexamples. (English) Zbl 1534.60153 Electron. J. Probab. 28, Paper No. 62, 43 p. (2023). MSC: 60K35 60G15 60G60 82B43 × Cite Format Result Cite Review PDF Full Text: DOI arXiv Link
Eisenbaum, Nathalie; Kaspi, Haya Addendum to: “Isomorphism theorems, extended Markov processes and random interlacements”. (English) Zbl 1515.60263 Electron. J. Probab. 28, Paper No. 45, 3 p. (2023). MSC: 60J25 60G15 60G57 60J35 60J40 60J45 60J55 × Cite Format Result Cite Review PDF Full Text: DOI Link
Sznitman, Alain-Sol On the cost of the bubble set for random interlacements. (English) Zbl 1528.60105 Invent. Math. 233, No. 2, 903-950 (2023). Reviewer: Janosch Ortmann (Montréal) MSC: 60K35 60F10 82B43 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Hernández-Torres, Saraí; Procaccia, Eviatar B.; Rosenthal, Ron The chemical distance in random interlacements in the low-intensity regime. (English) Zbl 1511.60145 Commun. Math. Phys. 400, No. 3, 1697-1737 (2023). MSC: 60K35 82B43 92E10 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Cai, Zhenhao; Han, Xiao; Ye, Jiayan; Zhang, Yuan On chemical distance and local uniqueness of a sufficiently supercritical finitary random interlacements. (English) Zbl 1525.60109 J. Theor. Probab. 36, No. 1, 522-592 (2023). MSC: 60K35 60G50 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Cai, Zhenhao; Zhang, Yuan On the exact orders of critical value in finitary random interlacements. (English) Zbl 1509.60166 Stochastic Processes Appl. 159, 391-427 (2023). MSC: 60K35 82B41 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Eisenbaum, Nathalie; Kaspi, Haya Isomorphism theorems, extended Markov processes and random interlacements. (English) Zbl 1509.60130 Electron. J. Probab. 27, Paper No. 160, 27 p. (2022); addendum ibid. 28, Paper No. 45, 3 p. (2023). . Link to issue. MSC: 60J25 60G15 60G57 60J35 60J40 60J45 60J55 × Cite Format Result Cite Review PDF Full Text: DOI
Cai, Zhenhao; Procaccia, Eviatar B.; Zhang, Yuan Continuity and uniqueness of percolation critical parameters in finitary random interlacements. (English) Zbl 1507.60125 Electron. J. Probab. 27, Paper No. 97, 46 p. (2022). MSC: 60K35 60D05 60G55 × Cite Format Result Cite Review PDF Full Text: DOI arXiv Link
Sznitman, Alain-Sol Excess deviations for points disconnected by random interlacements. (English) Zbl 1483.60149 Probab. Math. Phys. 2, No. 3, 563-611 (2021). MSC: 60K35 35A15 60F10 82B43 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Cai, Zhenhao; Zhang, Yuan Some rigorous results on the phase transition of finitary random interlacements. (English) Zbl 1493.60140 Electron. Commun. Probab. 26, Paper No. 52, 11 p. (2021). MSC: 60K35 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Sznitman, Alain-Sol On the \(C^1\)-property of the percolation function of random interlacements and a related variational problem. (English) Zbl 1469.60347 Vares, Maria Eulália (ed.) et al., In and out of equilibrium 3: celebrating Vladas Sidoravicius. Cham: Birkhäuser. Prog. Probab. 77, 775-796 (2021). MSC: 60K35 35A15 82B43 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Zhuang, Zijie On the percolative properties of the intersectionof two independent interlacements. (English) Zbl 1469.60143 ALEA, Lat. Am. J. Probab. Math. Stat. 18, No. 2, 1061-1084 (2021). MSC: 60G50 60K35 82B43 × Cite Format Result Cite Review PDF Full Text: arXiv Link
Procaccia, Eviatar B.; Ye, Jiayan; Zhang, Yuan Percolation for the finitary random interlacements of random spherical harmonics. (English) Zbl 1468.60123 ALEA, Lat. Am. J. Probab. Math. Stat. 18, No. 1, 265-287 (2021). MSC: 60K35 82B43 × Cite Format Result Cite Review PDF Full Text: arXiv Link
Li, Xinyi Percolative properties of Brownian interlacements and its vacant set. (English) Zbl 1469.60256 J. Theor. Probab. 33, No. 4, 1855-1893 (2020). MSC: 60J65 60K35 82B43 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Nitzschner, Maximilian; Sznitman, Alain-Sol Solidification of porous interfaces and disconnection. (English) Zbl 1475.60145 J. Eur. Math. Soc. (JEMS) 22, No. 8, 2629-2672 (2020). Reviewer: Ivan Podvigin (Novosibirsk) MSC: 60J45 60F10 60K35 82B43 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Chiarini, Alberto; Nitzschner, Maximilian Entropic repulsion for the occupation-time field of random interlacements conditioned on disconnection. (English) Zbl 1456.60189 Ann. Probab. 48, No. 3, 1317-1351 (2020). MSC: 60J27 60K35 60F10 60G60 82B43 × Cite Format Result Cite Review PDF Full Text: DOI arXiv Euclid
Hutchcroft, Tom Universality of high-dimensional spanning forests and sandpiles. (English) Zbl 1434.60296 Probab. Theory Relat. Fields 176, No. 1-2, 533-597 (2020). MSC: 60K35 82B20 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
de Bernardini, Diego F.; Gallesco, Christophe; Popov, Serguei An improved decoupling inequality for random interlacements. (English) Zbl 1428.60136 J. Stat. Phys. 177, No. 6, 1216-1239 (2019). MSC: 60K35 60G50 82C41 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Elias, Olof; Tykesson, Johan Visibility in the vacant set of the Brownian interlacements and the Brownian excursion process. (English) Zbl 1488.60231 ALEA, Lat. Am. J. Probab. Math. Stat. 16, No. 2, 1007-1028 (2019). MSC: 60K35 82B43 × Cite Format Result Cite Review PDF Full Text: arXiv Link
Sznitman, Alain-Sol On macroscopic holes in some supercritical strongly dependent percolation models. (English) Zbl 1467.60081 Ann. Probab. 47, No. 4, 2459-2493 (2019). MSC: 60K35 60G50 60F10 60G15 82B43 × Cite Format Result Cite Review PDF Full Text: DOI arXiv Euclid
Gantert, Nina; Popov, Serguei; Vachkovskaia, Marina On the range of a two-dimensional conditioned simple random walk. (Sur l’amplitude d’une marche aléatoire simple bidimensionnelle conditionnée.) (English) Zbl 1454.60110 Ann. Henri Lebesgue 2, 349-368 (2019). MSC: 60J10 60G50 82C41 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Sznitman, Alain-Sol On coupling and “Vacant set level set” percolation. (English) Zbl 1412.60135 Electron. Commun. Probab. 24, Paper No. 20, 12 p. (2019). MSC: 60K35 60G15 60J10 82B43 × Cite Format Result Cite Review PDF Full Text: DOI arXiv Euclid
Procaccia, Eviatar B.; Zhang, Yuan Connectivity properties of branching interlacements. (English) Zbl 1406.60121 ALEA, Lat. Am. J. Probab. Math. Stat. 16, No. 1, 279-314 (2019). MSC: 60J80 60D05 60G57 × Cite Format Result Cite Review PDF Full Text: arXiv Link
Drewitz, Alexander; Prévost, Alexis; Rodriguez, Pierre-François The sign clusters of the massless Gaussian free field percolate on \(\mathbb{Z}^{d}\), \(d \geqslant 3\) (and more). (English) Zbl 1394.60099 Commun. Math. Phys. 362, No. 2, 513-546 (2018). MSC: 60K35 82B43 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Alves, Caio; Popov, Serguei Conditional decoupling of random interlacements. (English) Zbl 1394.60095 ALEA, Lat. Am. J. Probab. Math. Stat. 15, No. 2, 1027-1063 (2018). MSC: 60K35 60G50 82C41 × Cite Format Result Cite Review PDF Full Text: arXiv Link
Camargo, Darcy; Popov, Serguei A one-dimensional version of the random interlacements. (English) Zbl 1388.60088 Stochastic Processes Appl. 128, No. 8, 2750-2778 (2018). MSC: 60G50 60K35 60F05 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Abächerli, Angelo; Sznitman, Alain-Sol Level-set percolation for the Gaussian free field on a transient tree. (English. French summary) Zbl 1396.60099 Ann. Inst. Henri Poincaré, Probab. Stat. 54, No. 1, 173-201 (2018). MSC: 60K35 60G15 60J10 60J80 82B43 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Comets, Francis; Popov, Serguei The vacant set of two-dimensional critical random interlacement is infinite. (English) Zbl 1409.60140 Ann. Probab. 45, No. 6B, 4752-4785 (2017). MSC: 60K35 60G50 82C41 × Cite Format Result Cite Review PDF Full Text: DOI arXiv Euclid
Li, Xinyi A lower bound for disconnection by simple random walk. (English) Zbl 1421.60002 Ann. Probab. 45, No. 2, 879-931 (2017). Reviewer: Dominique Lépingle (Orléans) MSC: 60F10 60K35 60J27 82B43 × Cite Format Result Cite Review PDF Full Text: DOI arXiv Euclid
Georgakopoulos, Agelos Group-walk random graphs. (English) Zbl 1371.05268 Ceccherini-Silberstein, Tullio (ed.) et al., Groups, graphs and random walks. Selected papers of the workshop, Cortona, Italy, June 2–6, 2014 on the occasion of the 60th birthday of Wolfgang Woess. Cambridge: Cambridge University Press (ISBN 978-1-316-60440-3/pbk; 978-1-316-57657-1/ebook). London Mathematical Society Lecture Note Series 436, 190-204 (2017). MSC: 05C80 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Sapozhnikov, Artem Random walks on infinite percolation clusters in models with long-range correlations. (English) Zbl 1374.60194 Ann. Probab. 45, No. 3, 1842-1898 (2017). Reviewer: Anatoliy Swishchuk (Calgary) MSC: 60K37 58J35 60K35 60G50 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Sznitman, Alain-Sol Disconnection, random walks, and random interlacements. (English) Zbl 1365.60080 Probab. Theory Relat. Fields 167, No. 1-2, 1-44 (2017). Reviewer: Boris Granovsky (Haifa) MSC: 60K35 60G50 60G55 60F10 60J27 82B43 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Černý, Jiří; Teixeira, Augusto Random walks on torus and random interlacements: macroscopic coupling and phase transition. (English) Zbl 1353.60083 Ann. Appl. Probab. 26, No. 5, 2883-2914 (2016). MSC: 60K35 60G50 82C41 05C80 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Lupu, Titus From loop clusters and random interlacements to the free field. (English) Zbl 1348.60141 Ann. Probab. 44, No. 3, 2117-2146 (2016). Reviewer: Boris Granovsky (Haifa) MSC: 60K35 60G15 60G60 60J75 60G55 05C90 × Cite Format Result Cite Review PDF Full Text: DOI arXiv Euclid
Černý, Jiří; Sapozhnikov, Artem Mixing time for the random walk on the range of the random walk on tori. (English) Zbl 1338.60240 Electron. Commun. Probab. 21, Paper No. 26, 10 p. (2016). MSC: 60K37 58J35 × Cite Format Result Cite Review PDF Full Text: DOI arXiv Euclid
Sznitman, Alain-Sol Coupling and an application to level-set percolation of the Gaussian free field. (English) Zbl 1336.60194 Electron. J. Probab. 21, Paper No. 35, 26 p. (2016). MSC: 60K35 60G15 60J27 60J80 82B43 × Cite Format Result Cite Review PDF Full Text: DOI arXiv Euclid
Comets, Francis; Popov, Serguei; Vachkovskaia, Marina Two-dimensional random interlacements and late points for random walks. (English) Zbl 1336.60185 Commun. Math. Phys. 343, No. 1, 129-164 (2016). MSC: 60K35 60G50 × Cite Format Result Cite Review PDF Full Text: DOI arXiv HAL
Drewitz, Alexander; Erhard, Dirk Transience of the vacant set for near-critical random interlacements in high dimensions. (English. French summary) Zbl 1333.60202 Ann. Inst. Henri Poincaré, Probab. Stat. 52, No. 1, 84-101 (2016). MSC: 60K35 60G55 82B43 × Cite Format Result Cite Review PDF Full Text: DOI arXiv Euclid
De Bernardini, Diego F.; Popov, Serguei Russo’s formula for random interlacements. (English) Zbl 1357.60108 J. Stat. Phys. 160, No. 2, 321-335 (2015). MSC: 60K35 60G50 82C41 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Rosen, Jay Isomorphism theorems: Markov processes, Gaussian processes and beyond. (English) Zbl 1338.60193 Gayrard, Véronique (ed.) et al., Correlated random systems: five different methods. CIRM Jean-Morlet Chair, Marseille, France, spring 2013. Cham: Springer; Paris: Société Mathématique de France (SMF) (ISBN 978-3-319-17673-4/pbk; 978-3-319-17674-1/ebook). Lecture Notes in Mathematics 2143, 121-177 (2015). MSC: 60J25 60G15 60K35 60J55 60G17 × Cite Format Result Cite Review PDF Full Text: DOI
Sznitman, Alain-Sol Disconnection and level-set percolation for the Gaussian free field. (English) Zbl 1337.60246 J. Math. Soc. Japan 67, No. 4, 1801-1843 (2015). Reviewer: Weiping Li (Stillwater) MSC: 60K35 60G60 60G15 60G50 60F10 82B43 × Cite Format Result Cite Review PDF Full Text: DOI arXiv Euclid
Popov, Serguei; Teixeira, Augusto Soft local times and decoupling of random interlacements. (English) Zbl 1329.60342 J. Eur. Math. Soc. (JEMS) 17, No. 10, 2545-2593 (2015). MSC: 60K35 60J10 60J55 60G50 82C41 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Popov, Serguei; Ráth, Balázs On decoupling inequalities and percolation of excursion sets of the Gaussian free field. (English) Zbl 1328.82026 J. Stat. Phys. 159, No. 2, 312-320 (2015). MSC: 82B43 60K35 × Cite Format Result Cite Review PDF Full Text: DOI arXiv Link
Wassmer, Tobias Phase transition for the vacant set left by random walk on the giant component of a random graph. (English. French summary) Zbl 1312.05126 Ann. Inst. Henri Poincaré, Probab. Stat. 51, No. 2, 756-780 (2015). MSC: 05C81 05C80 60J10 60K35 × Cite Format Result Cite Review PDF Full Text: DOI arXiv Euclid
Li, Xinyi; Sznitman, Alain-Sol Large deviations for occupation time profiles of random interlacements. (English) Zbl 1314.60078 Probab. Theory Relat. Fields 161, No. 1-2, 309-350 (2015). Reviewer: Neville Weber (Sydney) MSC: 60F10 60G60 60K35 60J45 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Ráth, Balázs A short proof of the phase transition for the vacant set of random interlacements. (English) Zbl 1307.60146 Electron. Commun. Probab. 20, Paper No. 3, 11 p. (2015). MSC: 60K35 82B43 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Drewitz, Alexander; Ráth, Balázs; Sapozhnikov, Artëm Local percolative properties of the vacant set of random interlacements with small intensity. (English. French summary) Zbl 1319.60180 Ann. Inst. Henri Poincaré, Probab. Stat. 50, No. 4, 1165-1197 (2014). MSC: 60K35 60G50 82B43 × Cite Format Result Cite Review PDF Full Text: DOI arXiv Euclid
Procaccia, Eviatar B.; Shellef, Eric On the range of a random walk in a torus and random interlacements. (English) Zbl 1305.60106 Ann. Probab. 42, No. 4, 1590-1634 (2014). MSC: 60K35 60G50 60K37 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Rodriguez, Pierre-François Level set percolation for random interlacements and the Gaussian free field. (English) Zbl 1288.60129 Stochastic Processes Appl. 124, No. 4, 1469-1502 (2014). MSC: 60K35 82B43 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Li, Xinyi; Sznitman, Alain-Sol A lower bound for disconnection by random interlacements. (English) Zbl 1355.60035 Electron. J. Probab. 19, Paper No. 17, 26 p. (2014). MSC: 60F10 60K35 60J27 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Sznitman, Alain-Sol On scaling limits and Brownian interlacements. (English) Zbl 1303.60022 Bull. Braz. Math. Soc. (N.S.) 44, No. 4, 555-592 (2013). Reviewer: Ivan Podvigin (Novosibirsk) MSC: 60F05 60J65 60G60 60J27 × Cite Format Result Cite Review PDF Full Text: DOI arXiv Link
Ráth, Balázs; Sapozhnikov, Artëm The effect of small quenched noise on connectivity properties of random interlacements. (English) Zbl 1347.60132 Electron. J. Probab. 18, Paper No. 4, 20 p. (2013). Reviewer: Michele Gianfelice (Rende) MSC: 60K35 82B43 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Teixeira, Augusto; Tykesson, Johan Random interlacements and amenability. (English) Zbl 1375.60139 Ann. Appl. Probab. 23, No. 3, 923-956 (2013). MSC: 60K35 82C41 × Cite Format Result Cite Review PDF Full Text: DOI arXiv Euclid
Sznitman, Alain-Sol On \({(\mathbb Z / N\mathbb Z)}^2\)-occupation times, the Gaussian free field, and random interlacements. (English) Zbl 1307.60103 Bull. Inst. Math., Acad. Sin. (N.S.) 7, No. 4, 565-602 (2012). MSC: 60J27 60F05 60G15 × Cite Format Result Cite Review PDF
Černý, Jiří; Teixeira, Augusto Quadros From random walk trajectories to random interlacements. (English) Zbl 1269.60002 Ensaios Matemáticos 23. Rio de Janeiro: Sociedade Brasileira de Matemática (ISBN 978-85-85818-69-2/pbk). 77 p. (2012). MSC: 60-02 60G50 60K35 05C81 × Cite Format Result Cite Review PDF Full Text: EMIS
Tykesson, Johan; Windisch, David Percolation in the vacant set of Poisson cylinders. (English) Zbl 1263.82027 Probab. Theory Relat. Fields 154, No. 1-2, 165-191 (2012). Reviewer: Piotr Garbaczewski (Opole) MSC: 82B43 60K35 60G55 82C41 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Sznitman, Alain-Sol Random interlacements and the Gaussian free field. (English) Zbl 1261.60095 Ann. Probab. 40, No. 6, 2400-2438 (2012). Reviewer: Anatoliy Pogorui (Zhytomyr) MSC: 60K35 60J27 60F05 × Cite Format Result Cite Review PDF Full Text: DOI arXiv Euclid
Sznitman, Alain-Sol An isomorphism theorem for random interlacements. (English) Zbl 1247.60135 Electron. Commun. Probab. 17, Paper No. 9, 9 p. (2012). MSC: 60K35 60J27 60G15 60F05 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Sznitman, Alain-Sol Topics in occupation times and Gaussian free fields. (English) Zbl 1246.60003 Zurich Lectures in Advanced Mathematics. Zürich: European Mathematical Society (EMS) (ISBN 978-3-03719-109-5/pbk). vii, 114 p. (2012). Reviewer: Utkir Rozikov (Tashkent) MSC: 60-01 60G15 60J27 60K35 82B41 × Cite Format Result Cite Review PDF Full Text: DOI Link
Belius, David Cover levels and random interlacements. (English) Zbl 1271.60057 Ann. Appl. Probab. 22, No. 2, 522-540 (2012). Reviewer: Achim Klenke (Mainz) MSC: 60G50 82C41 60D05 × Cite Format Result Cite Review PDF Full Text: DOI arXiv Euclid
Sznitman, Alain-Sol Decoupling inequalities and interlacement percolation on \(G\times \mathbb Z\). (English) Zbl 1277.60183 Invent. Math. 187, No. 3, 645-706 (2012). MSC: 60K35 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Ben Procaccia, Eviatar; Tykesson, Johan Geometry of the random interlacement. (English) Zbl 1254.60018 Electron. Commun. Probab. 16, 528-544 (2011). MSC: 60D05 60K35 60G55 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Sznitman, Alain-Sol A lower bound on the critical parameter of interlacement percolation in high dimension. (English) Zbl 1230.60103 Probab. Theory Relat. Fields 150, No. 3-4, 575-611 (2011). Reviewer: Piotr Garbaczewski (Opole) MSC: 60K35 60G50 82C41 × Cite Format Result Cite Review PDF Full Text: DOI arXiv Link
Teixeira, Augusto On the size of a finite vacant cluster of random interlacements with small intensity. (English) Zbl 1231.60117 Probab. Theory Relat. Fields 150, No. 3-4, 529-574 (2011). Reviewer: Anatoliy Pogorui (Zhytomyr) MSC: 60K35 82C41 × Cite Format Result Cite Review PDF Full Text: DOI arXiv Link
Sznitman, Alain-Sol On the critical parameter of interlacement percolation in high dimension. (English) Zbl 1210.60047 Ann. Probab. 39, No. 1, 70-103 (2011). Reviewer: Guy Jumarie (Montréal) MSC: 60G50 60K35 82C41 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Sidoravicius, Vladas; Sznitman, Alain-Sol Connectivity bounds for the vacant set of random interlacements. (English) Zbl 1210.60107 Ann. Inst. Henri Poincaré, Probab. Stat. 46, No. 4, 976-990 (2010). MSC: 60K35 60G50 82C41 × Cite Format Result Cite Review PDF Full Text: DOI arXiv EuDML
Windisch, David Random walks on discrete cylinders with large bases and random interlacements. (English) Zbl 1191.60062 Ann. Probab. 38, No. 2, 841-895 (2010). Reviewer: Piotr Garbaczewski (Opole) MSC: 60G50 60K35 82C41 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Sznitman, Alain-Sol On the domination of a random walk on a discrete cylinder by random interlacements. (English) Zbl 1196.60170 Electron. J. Probab. 14, 1670-1704 (2009). MSC: 60K35 60G50 82C41 × Cite Format Result Cite Review PDF Full Text: DOI arXiv EuDML EMIS
Teixeira, Augusto Interlacement percolation on transient weighted graphs. (English) Zbl 1192.60108 Electron. J. Probab. 14, 1604-1627 (2009). MSC: 60K35 82C41 × Cite Format Result Cite Review PDF Full Text: DOI arXiv EuDML EMIS
Sznitman, Alain-Sol Upper bound on the disconnection time of discrete cylinders and random interlacements. (English) Zbl 1179.60025 Ann. Probab. 37, No. 5, 1715-1746 (2009). Reviewer: Guy Jumarie (Montréal) MSC: 60G50 60K35 82C41 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Teixeira, Augusto On the uniqueness of the infinite cluster of the vacant set of random interlacements. (English) Zbl 1158.60046 Ann. Appl. Probab. 19, No. 1, 454-466 (2009). MSC: 60K35 82C41 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Windisch, David Random walk on a discrete torus and random interlacements. (English) Zbl 1187.60089 Electron. Commun. Probab. 13, 140-150 (2008). MSC: 60K35 60G50 82C41 × Cite Format Result Cite Review PDF Full Text: DOI arXiv EuDML EMIS