Rodriguez, Pierre-François On pinned fields, interlacements, and random walk on \(({\mathbb {Z}}/N {\mathbb {Z}})^2\). (English) Zbl 1411.60040 Probab. Theory Relat. Fields 173, No. 3-4, 1265-1299 (2019). MSC: 60F05 60G15 60K35 PDF BibTeX XML Cite \textit{P.-F. Rodriguez}, Probab. Theory Relat. Fields 173, No. 3--4, 1265--1299 (2019; Zbl 1411.60040) Full Text: DOI
Cooper, Colin; Frieze, Alan Vacant sets and vacant nets: component structures induced by a random walk. (English) Zbl 1329.05261 SIAM J. Discrete Math. 30, No. 1, 166-205 (2016). MSC: 05C80 05C81 PDF BibTeX XML Cite \textit{C. Cooper} and \textit{A. Frieze}, SIAM J. Discrete Math. 30, No. 1, 166--205 (2016; Zbl 1329.05261) Full Text: DOI arXiv
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 PDF BibTeX XML Cite \textit{T. Wassmer}, Ann. Inst. Henri Poincaré, Probab. Stat. 51, No. 2, 756--780 (2015; Zbl 1312.05126) Full Text: DOI Euclid 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 PDF BibTeX XML Cite \textit{A. Drewitz} et al., Ann. Inst. Henri Poincaré, Probab. Stat. 50, No. 4, 1165--1197 (2014; Zbl 1319.60180) Full Text: DOI Euclid
Goodman, Jesse; Den Hollander, Frank Extremal geometry of a Brownian porous medium. (English) Zbl 1327.60037 Probab. Theory Relat. Fields 160, No. 1-2, 127-174 (2014). Reviewer: N. G. Gamkrelidze (Moskva) MSC: 60D05 60F10 60J65 PDF BibTeX XML Cite \textit{J. Goodman} and \textit{F. Den Hollander}, Probab. Theory Relat. Fields 160, No. 1--2, 127--174 (2014; Zbl 1327.60037) Full Text: DOI arXiv
Drewitz, Alexander; Ráth, Balázs; Sapozhnikov, Artëm On chemical distances and shape theorems in percolation models with long-range correlations. (English) Zbl 1301.82027 J. Math. Phys. 55, No. 8, 083307, 30 p. (2014). MSC: 82B43 60K35 82B41 PDF BibTeX XML Cite \textit{A. Drewitz} et al., J. Math. Phys. 55, No. 8, 083307, 30 p. (2014; Zbl 1301.82027) Full Text: DOI arXiv
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 PDF BibTeX XML Cite \textit{E. B. Procaccia} and \textit{E. Shellef}, Ann. Probab. 42, No. 4, 1590--1634 (2014; Zbl 1305.60106) Full Text: DOI arXiv
Černý, Jiří; Teixeira, Augusto Critical window for the vacant set left by random walk on random regular graphs. (English) Zbl 1273.05209 Random Struct. Algorithms 43, No. 3, 313-337 (2013). MSC: 05C81 05C80 60G50 60K35 PDF BibTeX XML Cite \textit{J. Černý} and \textit{A. Teixeira}, Random Struct. Algorithms 43, No. 3, 313--337 (2013; Zbl 1273.05209) Full Text: DOI
Cooper, Colin; Frieze, Alan Component structure of the vacant set induced by a random walk on a random graph. (English) Zbl 1259.05155 Random Struct. Algorithms 42, No. 2, 135-158 (2013). MSC: 05C81 05C80 PDF BibTeX XML Cite \textit{C. Cooper} and \textit{A. Frieze}, Random Struct. Algorithms 42, No. 2, 135--158 (2013; Zbl 1259.05155) Full Text: DOI arXiv
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 PDF BibTeX XML Cite \textit{A.-S. Sznitman}, Invent. Math. 187, No. 3, 645--706 (2012; Zbl 1277.60183) Full Text: DOI arXiv
Černý, Jiří; Teixeira, Augusto; Windisch, David Giant vacant component left by a random walk in a random \(d\)-regular graph. (English. French summary) Zbl 1267.05237 Ann. Inst. Henri Poincaré, Probab. Stat. 47, No. 4, 929-968 (2011). Reviewer: Ove Frank (Stockholm) MSC: 05C81 60G50 05C80 82B41 PDF BibTeX XML Cite \textit{J. Černý} et al., Ann. Inst. Henri Poincaré, Probab. Stat. 47, No. 4, 929--968 (2011; Zbl 1267.05237) Full Text: DOI Euclid arXiv
Teixeira, Augusto; Windisch, David On the fragmentation of a torus by random walk. (English) Zbl 1235.60143 Commun. Pure Appl. Math. 64, No. 12, 1599-1646 (2011). Reviewer: Guy Jumarie (Montréal) MSC: 60K35 60G50 82C41 05C81 PDF BibTeX XML Cite \textit{A. Teixeira} and \textit{D. Windisch}, Commun. Pure Appl. Math. 64, No. 12, 1599--1646 (2011; Zbl 1235.60143) Full Text: DOI arXiv
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 PDF BibTeX XML Cite \textit{A. Teixeira}, Probab. Theory Relat. Fields 150, No. 3--4, 529--574 (2011; Zbl 1231.60117) Full Text: DOI arXiv
Jara, Milton; Landim, Claudio; Teixeira, Augusto Quenched scaling limits of trap models. (English) Zbl 1211.60040 Ann. Probab. 39, No. 1, 176-223 (2011). Reviewer: Guy Jumarie (Montréal) MSC: 60K37 60G50 60J27 60K35 82C05 82D30 82C41 PDF BibTeX XML Cite \textit{M. Jara} et al., Ann. Probab. 39, No. 1, 176--223 (2011; Zbl 1211.60040) Full Text: DOI
Sznitman, Alain-Sol Vacant set of random interlacements and percolation. (English) Zbl 1202.60160 Ann. Math. (2) 171, No. 3, 2039-2087 (2010). Reviewer: Anatoliy Pogorui (Zhytomyr) MSC: 60K35 60G50 82C41 PDF BibTeX XML Cite \textit{A.-S. Sznitman}, Ann. Math. (2) 171, No. 3, 2039--2087 (2010; Zbl 1202.60160) Full Text: DOI Link 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 PDF BibTeX XML Cite \textit{A. Teixeira}, Ann. Appl. Probab. 19, No. 1, 454--466 (2009; Zbl 1158.60046) Full Text: DOI arXiv
Windisch, David On the disconnection of a discrete cylinder by a biased random walk. (English) Zbl 1148.60028 Ann. Appl. Probab. 18, No. 4, 1441-1490 (2008). Reviewer: Aurel Spătaru (Bucureşti) MSC: 60G50 60D05 PDF BibTeX XML Cite \textit{D. Windisch}, Ann. Appl. Probab. 18, No. 4, 1441--1490 (2008; Zbl 1148.60028) Full Text: DOI arXiv