Aïdékon, Elie; Hu, Yueyun; Shi, Zhan An infinite-dimensional representation of the Ray-Knight theorems. (English) Zbl 07791015 Sci. China, Math. 67, No. 1, 149-162 (2024). MSC: 60J65 60J55 60G40 60J80 PDFBibTeX XMLCite \textit{E. Aïdékon} et al., Sci. China, Math. 67, No. 1, 149--162 (2024; Zbl 07791015) Full Text: DOI arXiv
Chen, Xinxing; Hu, Yueyun; Shi, Zhan The sustainability probability for the critical Derrida-Retaux model. (English) Zbl 1489.60137 Probab. Theory Relat. Fields 182, No. 1-2, 641-684 (2022). Reviewer: Utkir A. Rozikov (Tashkent) MSC: 60J80 82B27 82B26 PDFBibTeX XMLCite \textit{X. Chen} et al., Probab. Theory Relat. Fields 182, No. 1--2, 641--684 (2022; Zbl 1489.60137) Full Text: DOI arXiv
Chen, Xinxing; Shi, Zhan The stable Derrida-Retaux system at criticality. (English) Zbl 1469.60317 Vares, Maria Eulália (ed.) et al., In and out of equilibrium 3: celebrating Vladas Sidoravicius. Cham: Birkhäuser. Prog. Probab. 77, 239-264 (2021). MSC: 60K35 60J80 82B27 PDFBibTeX XMLCite \textit{X. Chen} and \textit{Z. Shi}, Prog. Probab. 77, 239--264 (2021; Zbl 1469.60317) Full Text: DOI arXiv
Chen, Xinxing; Dagard, Victor; Derrida, Bernard; Hu, Yueyun; Lifshits, Mikhail; Shi, Zhan The Derrida-Retaux conjecture on recursive models. (English) Zbl 1484.60096 Ann. Probab. 49, No. 2, 637-670 (2021). Reviewer: A. C. D. van Enter (Groningen) MSC: 60J80 60K35 82B27 PDFBibTeX XMLCite \textit{X. Chen} et al., Ann. Probab. 49, No. 2, 637--670 (2021; Zbl 1484.60096) Full Text: DOI arXiv
Chen, Xinxing; Dagard, Victor; Derrida, Bernard; Shi, Zhan The critical behaviors and the scaling functions of a coalescence equation. (English) Zbl 1514.82101 J. Phys. A, Math. Theor. 53, No. 19, Article ID 195202, 25 p. (2020). MSC: 82B44 PDFBibTeX XMLCite \textit{X. Chen} et al., J. Phys. A, Math. Theor. 53, No. 19, Article ID 195202, 25 p. (2020; Zbl 1514.82101) Full Text: DOI arXiv
Derrida, Bernard; Shi, Zhan Results and conjectures on a toy model of depinning. (English) Zbl 1473.60122 Mosc. Math. J. 20, No. 4, 695-709 (2020). MSC: 60J80 82B27 PDFBibTeX XMLCite \textit{B. Derrida} and \textit{Z. Shi}, Mosc. Math. J. 20, No. 4, 695--709 (2020; Zbl 1473.60122) Full Text: arXiv Link
Chen, Xinxing; Derrida, Bernard; Hu, Yueyun; Lifshits, Mikhail; Shi, Zhan A max-type recursive model: some properties and open questions. (English) Zbl 1446.82024 Sidoravicius, Vladas (ed.), Sojourns in probability theory and statistical physics. III. Interacting particle systems and random walks, a festschrift for Charles M. Newman. Singapore: Springer; Shanghai: NYU Shanghai. Springer Proc. Math. Stat. 300, 166-186 (2019). MSC: 82B26 82B44 82B27 82B28 82B20 PDFBibTeX XMLCite \textit{X. Chen} et al., Springer Proc. Math. Stat. 300, 166--186 (2019; Zbl 1446.82024) Full Text: DOI arXiv
Aïdékon, E.; Hu, Yueyun; Shi, Zhan Large deviations for level sets of a branching Brownian motion and Gaussian free fields. (English) Zbl 1478.60230 J. Math. Sci., New York 238, No. 4, 348-365 (2019) and Zap. Nauchn. Semin. POMI 457, 12-36 (2017). MSC: 60J80 60J65 60F10 60G15 PDFBibTeX XMLCite \textit{E. Aïdékon} et al., J. Math. Sci., New York 238, No. 4, 348--365 (2019; Zbl 1478.60230) Full Text: DOI arXiv
Hu, Yueyun; Shi, Zhan The free energy in the Derrida-Retaux recursive model. (English) Zbl 1400.82116 J. Stat. Phys. 172, No. 3, 718-741 (2018). MSC: 82B44 60J80 PDFBibTeX XMLCite \textit{Y. Hu} and \textit{Z. Shi}, J. Stat. Phys. 172, No. 3, 718--741 (2018; Zbl 1400.82116) Full Text: DOI arXiv
Derrida, Bernard; Shi, Zhan Slower deviations of the branching Brownian motion and of branching random walks. (English) Zbl 1377.60062 J. Phys. A, Math. Theor. 50, No. 34, Article ID 344001, 13 p. (2017). MSC: 60G70 60J80 60J65 60G50 PDFBibTeX XMLCite \textit{B. Derrida} and \textit{Z. Shi}, J. Phys. A, Math. Theor. 50, No. 34, Article ID 344001, 13 p. (2017; Zbl 1377.60062) Full Text: DOI arXiv
Berestycki, Julien; Brunet, Éric; Shi, Zhan Accessibility percolation with backsteps. (English) Zbl 1358.60101 ALEA, Lat. Am. J. Probab. Math. Stat. 14, No. 1, 45-62 (2017). MSC: 60K35 60J80 60G18 92D15 PDFBibTeX XMLCite \textit{J. Berestycki} et al., ALEA, Lat. Am. J. Probab. Math. Stat. 14, No. 1, 45--62 (2017; Zbl 1358.60101) Full Text: arXiv Link
Derrida, Bernard; Shi, Zhan Large deviations for the branching Brownian motion in presence of selection or coalescence. (English) Zbl 1346.82031 J. Stat. Phys. 163, No. 6, 1285-1311 (2016). MSC: 82C41 60F10 60J65 60J80 35Q92 PDFBibTeX XMLCite \textit{B. Derrida} and \textit{Z. Shi}, J. Stat. Phys. 163, No. 6, 1285--1311 (2016; Zbl 1346.82031) Full Text: DOI arXiv
Berestycki, Julien; Brunet, Éric; Shi, Zhan The number of accessible paths in the hypercube. (English) Zbl 1341.60103 Bernoulli 22, No. 2, 653-680 (2016). MSC: 60J80 60K35 92D15 PDFBibTeX XMLCite \textit{J. Berestycki} et al., Bernoulli 22, No. 2, 653--680 (2016; Zbl 1341.60103) Full Text: DOI arXiv Euclid
Aidekon, Elie; Shi, Zhan The Seneta-Heyde scaling for the branching random walk. (English) Zbl 1304.60092 Ann. Probab. 42, No. 3, 959-993 (2014). Reviewer: Heinrich Hering (Rockenberg) MSC: 60J80 60F05 PDFBibTeX XMLCite \textit{E. Aidekon} and \textit{Z. Shi}, Ann. Probab. 42, No. 3, 959--993 (2014; Zbl 1304.60092) Full Text: DOI arXiv Euclid
Faraud, Gabriel; Hu, Yueyun; Shi, Zhan Almost sure convergence for stochastically biased random walks on trees. (English) Zbl 1257.05162 Probab. Theory Relat. Fields 154, No. 3-4, 621-660 (2012). MSC: 05C81 60J80 60G50 60K37 PDFBibTeX XMLCite \textit{G. Faraud} et al., Probab. Theory Relat. Fields 154, No. 3--4, 621--660 (2012; Zbl 1257.05162) Full Text: DOI arXiv
Gantert, Nina; Hu, Yueyun; Shi, Zhan Asymptotics for the survival probability in a killed branching random walk. (English. French summary) Zbl 1210.60093 Ann. Inst. Henri Poincaré, Probab. Stat. 47, No. 1, 111-129 (2011). MSC: 60J80 PDFBibTeX XMLCite \textit{N. Gantert} et al., Ann. Inst. Henri Poincaré, Probab. Stat. 47, No. 1, 111--129 (2011; Zbl 1210.60093) Full Text: DOI arXiv EuDML
Aïdékon, Elie; Shi, Zhan Weak convergence for the minimal position in a branching random walk: a simple proof. (English) Zbl 1240.60227 Period. Math. Hung. 61, No. 1-2, 43-54 (2010). Reviewer: Heinrich Hering (Rockenberg) MSC: 60J80 PDFBibTeX XMLCite \textit{E. Aïdékon} and \textit{Z. Shi}, Period. Math. Hung. 61, No. 1--2, 43--54 (2010; Zbl 1240.60227) Full Text: DOI arXiv
Gantert, Nina; Peres, Yuval; Shi, Zhan The infinite valley for a recurrent random walk in random environment. (English) Zbl 1201.60096 Ann. Inst. Henri Poincaré, Probab. Stat. 46, No. 2, 525-536 (2010). Reviewer: Vitalii Gasanenko (Kyiv) MSC: 60K37 60J55 60F10 PDFBibTeX XMLCite \textit{N. Gantert} et al., Ann. Inst. Henri Poincaré, Probab. Stat. 46, No. 2, 525--536 (2010; Zbl 1201.60096) Full Text: DOI arXiv EuDML
Hu, Yueyun; Shi, Zhan Slow movement of random walk in random environment on a regular tree. (English) Zbl 1124.60083 Ann. Probab. 35, No. 5, 1978-1997 (2007). MSC: 60K37 60G50 60J80 PDFBibTeX XMLCite \textit{Y. Hu} and \textit{Z. Shi}, Ann. Probab. 35, No. 5, 1978--1997 (2007; Zbl 1124.60083) Full Text: DOI arXiv
Shi, Zhan; Zindy, Olivier A weakness in strong localization for Sinai’s walk. (English) Zbl 1117.60091 Ann. Probab. 35, No. 3, 1118-1140 (2007). MSC: 60K37 60G50 60J55 PDFBibTeX XMLCite \textit{Z. Shi} and \textit{O. Zindy}, Ann. Probab. 35, No. 3, 1118--1140 (2007; Zbl 1117.60091) Full Text: DOI arXiv
Dembo, Amir; Gantert, Nina; Peres, Yuval; Shi, Zhan Valleys and the maximum local time for random walk in random environment. (English) Zbl 1106.60082 Probab. Theory Relat. Fields 137, No. 3-4, 443-473 (2007). MSC: 60K37 60G50 60J55 60F10 PDFBibTeX XMLCite \textit{A. Dembo} et al., Probab. Theory Relat. Fields 137, No. 3--4, 443--473 (2007; Zbl 1106.60082) Full Text: DOI arXiv
Khoshnevisan, Davar; Révész, Pál; Shi, Zhan Level crossings of a two-parameter random walk. (English) Zbl 1072.60062 Stochastic Processes Appl. 115, No. 3, 359-380 (2005). Reviewer: Aleksander Iksanov (Kiev) MSC: 60J55 60G50 60F17 PDFBibTeX XMLCite \textit{D. Khoshnevisan} et al., Stochastic Processes Appl. 115, No. 3, 359--380 (2005; Zbl 1072.60062) Full Text: DOI
Hu, Yueyun; Shi, Zhan Moderate deviations for diffusions with Brownian potentials. (English) Zbl 1066.60096 Ann. Probab. 32, No. 4, 3191-3220 (2004). MSC: 60K37 60F10 PDFBibTeX XMLCite \textit{Y. Hu} and \textit{Z. Shi}, Ann. Probab. 32, No. 4, 3191--3220 (2004; Zbl 1066.60096) Full Text: DOI arXiv
Lifshits, Mikhail A.; Shi, Zhan The escape rate of favorite sites of simple random walk and Brownian motion. (English) Zbl 1067.60072 Ann. Probab. 32, No. 1A, 129-152 (2004). Reviewer: Peter Mörters (Bath) MSC: 60J55 60J65 60G15 PDFBibTeX XMLCite \textit{M. A. Lifshits} and \textit{Z. Shi}, Ann. Probab. 32, No. 1A, 129--152 (2004; Zbl 1067.60072) Full Text: DOI
Gantert, Nina; Shi, Zhan Many visits to a single site by a transient random walk in random environment. (English) Zbl 1059.60100 Stochastic Processes Appl. 99, No. 2, 159-176 (2002). Reviewer: Ivan Křivý (Ostrava) MSC: 60K37 60G50 60J55 60J80 PDFBibTeX XMLCite \textit{N. Gantert} and \textit{Z. Shi}, Stochastic Processes Appl. 99, No. 2, 159--176 (2002; Zbl 1059.60100) Full Text: DOI
Csáki, Endre; Révész, Pál; Shi, Zhan A strong invariance principle for two-dimensional random walk in random scenery. (English) Zbl 1047.60043 Stochastic Processes Appl. 92, No. 2, 181-200 (2001). Reviewer: Zuzana Prášková (Praha) MSC: 60G50 60F17 PDFBibTeX XMLCite \textit{E. Csáki} et al., Stochastic Processes Appl. 92, No. 2, 181--200 (2001; Zbl 1047.60043) Full Text: DOI
Csáki, Endre; Khoshnevisan, Davar; Shi, Zhan Boundary crossings and the distribution function of the maximum of Brownian sheet. (English) Zbl 1046.60048 Stochastic Processes Appl. 90, No. 1, 1-18 (2000). MSC: 60G60 60G17 PDFBibTeX XMLCite \textit{E. Csáki} et al., Stochastic Processes Appl. 90, No. 1, 1--18 (2000; Zbl 1046.60048) Full Text: DOI
Révész, Pál; Shi, Zhan Strong approximation of spatial random walk in random scenery. (English) Zbl 1045.60041 Stochastic Processes Appl. 88, No. 2, 329-345 (2000). Reviewer: František Matúš (Praha) MSC: 60G50 60F15 PDFBibTeX XMLCite \textit{P. Révész} and \textit{Z. Shi}, Stochastic Processes Appl. 88, No. 2, 329--345 (2000; Zbl 1045.60041) Full Text: DOI
Eisenbaum, Nathalie; Kaspi, Haya; Marcus, Michael B.; Rosen, Jay; Shi, Zhan A Ray-Knight theorem for symmetric Markov processes. (English) Zbl 1044.60064 Ann. Probab. 28, No. 4, 1781-1796 (2000). MSC: 60J55 60J25 PDFBibTeX XMLCite \textit{N. Eisenbaum} et al., Ann. Probab. 28, No. 4, 1781--1796 (2000; Zbl 1044.60064) Full Text: DOI
Khoshnevisan, Davar; Shi, Zhan Brownian sheet and capacity. (English) Zbl 0962.60066 Ann. Probab. 27, No. 3, 1135-1159 (1999). Reviewer: Liliana Popa (Iaşi) MSC: 60J45 60G60 31C15 60H07 60G17 47D07 PDFBibTeX XMLCite \textit{D. Khoshnevisan} and \textit{Z. Shi}, Ann. Probab. 27, No. 3, 1135--1159 (1999; Zbl 0962.60066) Full Text: DOI
Hu, Yueyun; Shi, Zhan; Yor, Marc Rates of convergence of diffusions with drifted Brownian potentials. (English) Zbl 0932.60083 Trans. Am. Math. Soc. 351, No. 10, 3915-3934 (1999). Reviewer: Nina Gantert (Berlin) MSC: 60J60 60F05 PDFBibTeX XMLCite \textit{Y. Hu} et al., Trans. Am. Math. Soc. 351, No. 10, 3915--3934 (1999; Zbl 0932.60083) Full Text: DOI
Hu, Yueyun; Shi, Zhan Favourite sites of transient Brownian motion. (English) Zbl 0942.60064 Stochastic Processes Appl. 73, No. 1, 87-99 (1998). Reviewer: P. Lachout (Praha) MSC: 60J65 60J55 60F15 PDFBibTeX XMLCite \textit{Y. Hu} and \textit{Z. Shi}, Stochastic Processes Appl. 73, No. 1, 87--99 (1998; Zbl 0942.60064) Full Text: DOI
Shi, Zhan A local time curiosity in random environment. (English) Zbl 0932.60054 Stochastic Processes Appl. 76, No. 2, 231-250 (1998). Reviewer: M.Janžura (Praha) MSC: 60G50 60J55 PDFBibTeX XMLCite \textit{Z. Shi}, Stochastic Processes Appl. 76, No. 2, 231--250 (1998; Zbl 0932.60054) Full Text: DOI
Hu, Yueyun; Shi, Zhan The limits of Sinai’s simple random walk in random environment. (English) Zbl 0936.60088 Ann. Probab. 26, No. 4, 1477-1521 (1998). MSC: 60K37 60J60 60F15 PDFBibTeX XMLCite \textit{Y. Hu} and \textit{Z. Shi}, Ann. Probab. 26, No. 4, 1477--1521 (1998; Zbl 0936.60088) Full Text: DOI
Shi, Zhan Windings of Brownian motion and random walks in the plane. (English) Zbl 0938.60073 Ann. Probab. 26, No. 1, 112-131 (1998). Reviewer: N.M.Zinchenko (Kyïv) MSC: 60J65 60G50 60F15 PDFBibTeX XMLCite \textit{Z. Shi}, Ann. Probab. 26, No. 1, 112--131 (1998; Zbl 0938.60073) Full Text: DOI
Khoshnevisan, Davar; Shi, Zhan Chung’s law for integrated Brownian motion. (English) Zbl 0902.60031 Trans. Am. Math. Soc. 350, No. 10, 4253-4264 (1998). MSC: 60G15 60J65 60J55 PDFBibTeX XMLCite \textit{D. Khoshnevisan} and \textit{Z. Shi}, Trans. Am. Math. Soc. 350, No. 10, 4253--4264 (1998; Zbl 0902.60031) Full Text: DOI
Shi, Zhan Brownian motion normalized by maximum local time. (English) Zbl 0889.60082 Stochastic Processes Appl. 65, No. 2, 217-231 (1996). Reviewer: Jan Seidler (Praha) MSC: 60J65 60J55 PDFBibTeX XMLCite \textit{Z. Shi}, Stochastic Processes Appl. 65, No. 2, 217--231 (1996; Zbl 0889.60082) Full Text: DOI
Shi, Z. Small ball probabilities for a Wiener process under weighted sup-norms, with an application to the supremum of Bessel local times. (English) Zbl 0959.60080 J. Theor. Probab. 9, No. 4, 915-929 (1996). MSC: 60J65 60J55 PDFBibTeX XMLCite \textit{Z. Shi}, J. Theor. Probab. 9, No. 4, 915--929 (1996; Zbl 0959.60080) Full Text: DOI
Shi, Z. On transient Bessel processes and planar Brownian motion reflected at their future infima. (English) Zbl 0851.60082 Stochastic Processes Appl. 60, No. 1, 87-102 (1995). Reviewer: Ph.Biane (Paris) MSC: 60J65 60G17 PDFBibTeX XMLCite \textit{Z. Shi}, Stochastic Processes Appl. 60, No. 1, 87--102 (1995; Zbl 0851.60082) Full Text: DOI
Hu, Y.; Shi, Z. Sojourns and future infima of planar Brownian motion. (English) Zbl 0833.60084 Probab. Theory Relat. Fields 103, No. 3, 329-348 (1995). MSC: 60J65 60G17 60F15 PDFBibTeX XMLCite \textit{Y. Hu} and \textit{Z. Shi}, Probab. Theory Relat. Fields 103, No. 3, 329--348 (1995; Zbl 0833.60084) Full Text: DOI
Hu, Y.; Shi, Z. The Csörgö-Révész modulus of non-differentiability of iterated Brownian motion. (English) Zbl 0833.60033 Stochastic Processes Appl. 58, No. 2, 267-279 (1995). Reviewer: H.Hering (Göttingen) MSC: 60F15 60G17 PDFBibTeX XMLCite \textit{Y. Hu} and \textit{Z. Shi}, Stochastic Processes Appl. 58, No. 2, 267--279 (1995; Zbl 0833.60033) Full Text: DOI
Shi, Z. Lower limits of iterated Wiener processes. (English) Zbl 0824.60025 Stat. Probab. Lett. 23, No. 3, 259-270 (1995). Reviewer: K.Kubilius (Vilnius) MSC: 60F15 60G17 60J60 PDFBibTeX XMLCite \textit{Z. Shi}, Stat. Probab. Lett. 23, No. 3, 259--270 (1995; Zbl 0824.60025) Full Text: DOI
Shi, Z. A generalization of the Chung-Mogul’skii law of the iterated logarithm. (English) Zbl 0732.60038 J. Multivariate Anal. 37, No. 2, 269-278 (1991). Reviewer: A.R.Dabrowski (Ottawa) MSC: 60F15 60J65 PDFBibTeX XMLCite \textit{Z. Shi}, J. Multivariate Anal. 37, No. 2, 269--278 (1991; Zbl 0732.60038) Full Text: DOI