Project Euclid

References

• [1] Andreoletti, P.: A limit result for a system of particles in random environment. J. Stat. Phys. 131 (2008), 235–246.
  Zentralblatt MATH: 1144.82027
  Digital Object Identifier: doi:10.1007/s10955-008-9497-z
  
• [2] Andreoletti, P. and Devulder, A.: Localization and number of visited valleys for a transient diffusion in random environment. Electron. J. Probab. 20 (2015), no. 56, 1–58.
  Zentralblatt MATH: 1321.60214
  Digital Object Identifier: doi:10.1214/EJP.v20-3173
  
• [3] Andreoletti, P., Devulder, A. and Véchambre, G.: Renewal structure and local time for diffusions in random environment. ALEA Lat. Am. J. Probab. Math. Stat. 13 (2016), 863–923.
  Zentralblatt MATH: 1350.60107
  
• [4] Barlow, M., Peres, Y. and Sousi, P.: Collisions of random walks Ann. Inst. H. Poincaré Probab. Stat. 48 (2012), no. 4, 922–946.
  Zentralblatt MATH: 1285.60073
  Digital Object Identifier: doi:10.1214/12-AIHP481
  Project Euclid: euclid.aihp/1353098434
  
• [5] Benjamini, I., Pemantle, R. and Peres, Y.: Martin capacity for Markov chains. Ann. Probab. 23 (1995), 1332–1346.
  Zentralblatt MATH: 0840.60068
  Digital Object Identifier: doi:10.1214/aop/1176988187
  Project Euclid: euclid.aop/1176988187
  
• [6] Bertoin, J.: Splitting at the infimum and excursions in half-lines for random walks and Lévy processes. Stochastic Process. Appl. 47 (1993), no. 1, 17–35.
  Zentralblatt MATH: 0786.60101
  Digital Object Identifier: doi:10.1016/0304-4149(93)90092-I
  
• [7] Brox, Th.: A one-dimensional diffusion process in a Wiener medium. Ann. Probab. 14 (1986), 1206–1218.
  Zentralblatt MATH: 0608.60072
  Digital Object Identifier: doi:10.1214/aop/1176992363
  Project Euclid: euclid.aop/1176992363
  
• [8] Campari, R. and Cassi, D.: Random collisions on branched networks: How simultaneous diffusion prevents encounters in inhomogeneous structures. Physical Review E 86 (2012), no. 2.
• [9] Chen, X. and Chen, D.: Two random walks on the open cluster of $ \mathbb{Z} ^{2}$ meet infinitely often. Science China Mathematics 53 (2010), 1971–1978.
  Zentralblatt MATH: 1216.05147
  Digital Object Identifier: doi:10.1007/s11425-010-4064-x
  
• [10] Chen, X. and Chen, D.: Some sufficient conditions for infinite collisions of simple random walks on a wedge comb. Electron. J. Probab. 16 (2011), no. 49, 1341–1355.
  Zentralblatt MATH: 1244.60069
  
• [11] Chen. D., Wei, B. and Zhang, F.: A note on the finite collision property of random walks. Statistics and Probability Letters 78 (2008), 1742–1747.
  Zentralblatt MATH: 1154.60301
  Digital Object Identifier: doi:10.1016/j.spl.2008.01.034
  
• [12] Chen, X.: Gaussian bounds and collisions of variable speed random walks on lattices with power law conductances. Stoch. Process Appl. 126 (2016), no. 10, 3041–3064.
  Zentralblatt MATH: 1375.60085
  Digital Object Identifier: doi:10.1016/j.spa.2016.03.011
  
• [13] Dembo, A., Gantert, N., Peres, Y., Shi, Z.: Valleys and the maximum local time for random walk in random environment. Probab. Theory Related Fields 137 (2007), 443–473.
  Zentralblatt MATH: 1106.60082
  Digital Object Identifier: doi:10.1007/s00440-006-0005-6
  
• [14] Devulder, A.: Persistence of some additive functionals of Sinai’s walk. Ann. Inst. H. Poincaré Probab. Stat. 52 (2016), 1076–1105.
  Zentralblatt MATH: 1350.60110
  Digital Object Identifier: doi:10.1214/15-AIHP679
  Project Euclid: euclid.aihp/1469723512
  
• [15] Devulder, A., Gantert, N., Pène, F.: Collisions of several walkers in recurrent random environments. Electron. J. Probab. 23 (2018), no. 90, 1–34.
  Zentralblatt MATH: 1414.60083
  Digital Object Identifier: doi:10.1214/18-EJP192
  
• [16] Dolgopyat, D. and Goldsheid, I.: Quenched limit theorems for nearest neighbour random walks in 1D random environment. Comm. Math. Phys. 315 (2012), 241–277.
  Zentralblatt MATH: 1260.60187
  Digital Object Identifier: doi:10.1007/s00220-012-1539-3
  
• [17] Dvoretzky, A. and Erdös, P.: Some problems on random walk in space. Proceedings of the Second Berkeley Symposium on Mathematical Statistics and Probability, 1950 (1951), 353–367, University of California Press, Berkeley and Los Angeles.
• [18] Enriquez, N., Sabot, C. and Zindy, O.: Limit laws for transient random walks in random environment on Z. Ann. Inst. Fourier (Grenoble) 59 (2009), no. 6, 2469–2508.
  Zentralblatt MATH: 1200.60093
  Digital Object Identifier: doi:10.5802/aif.2497
  
• [19] Enriquez, N., Sabot, C. and Zindy, O.: Aging and quenched localization for one dimensional random walks in random environment in the sub-ballistic regime. Bull. Soc. Math. France 137 (2009), 423–452.
  Zentralblatt MATH: 1186.60108
  Digital Object Identifier: doi:10.24033/bsmf.2580
  
• [20] Gallesco, C.: Meeting time of independent random walks in random environment. ESAIM Probab. Stat. 17 (2013), 257–292.
  Zentralblatt MATH: 1292.60098
  Digital Object Identifier: doi:10.1051/ps/2011159
  
• [21] Gantert, N., Kochler M. and Pène, F.: On the recurrence of some random walks in random environment. ALEA Lat. Am. J. Probab. Math. Stat. 11 (2014), 483–502.
  Zentralblatt MATH: 1301.60112
  
• [22] Golosov, A. O.: Localization of random walks in one-dimensional random environments. Comm. Math. Phys. 92 (1984), no. 4, 491–506.
  Zentralblatt MATH: 0534.60065
  Digital Object Identifier: doi:10.1007/BF01215280
  Project Euclid: euclid.cmp/1103940927
  
• [23] Hutchcroft, T. and Peres, Y.: Collisions of random walks in reversible random graphs. Electron. Commun. Probab. 20 (2015), no. 63, 1–6.
  Zentralblatt MATH: 1329.60357
  Digital Object Identifier: doi:10.1214/ECP.v20-4330
  
• [24] Iglehart, D.L.: Extreme values in the GI/G/1 queue. Ann. Math. Statist. 43 (1972), 627–635.
  Zentralblatt MATH: 0238.60072
  Digital Object Identifier: doi:10.1214/aoms/1177692642
  Project Euclid: euclid.aoms/1177692642
  
• [25] Jara M. and Peterson J.: Hydrodynamic limit for a system of independent, sub-ballistic random walks in a common random environment. Ann. Inst. Henri Poincaré Probab. Stat. 53 (2017), 1747–1792.
  Zentralblatt MATH: 1382.60121
  Digital Object Identifier: doi:10.1214/16-AIHP770
  Project Euclid: euclid.aihp/1511773725
  
• [26] Kesten, H., Kozlov, M.V. and Spitzer, F.: A limit law for random walk in a random environment. Compositio Math. 30 (1975), 145–168.
  Zentralblatt MATH: 0388.60069
  
• [27] Korshunov, D.: On distribution tail of the maximum of a random walk. Stochastic Process. Appl. 72 (1997), 97–103.
  Zentralblatt MATH: 0942.60018
  Digital Object Identifier: doi:10.1016/S0304-4149(97)00060-4
  
• [28] Krishnapur, M. and Peres, Y.: Recurrent graphs where two independent random walks collide finitely often. Electron. Comm. Probab 9 (2004), 72–81.
  Zentralblatt MATH: 1060.60044
  Digital Object Identifier: doi:10.1214/ECP.v9-1111
  
• [29] Neveu, J.: Bases mathématiques du calcul des probabilités, Masson et Cie éditeurs, Paris, 1964, xiii+203 pp.
• [30] Peterson, J.: Systems of one-dimensional random walks in a common random environment. Electron. J. Probab. 15 (2010), no. 32, 1024–1040.
  Zentralblatt MATH: 1225.60159
  Digital Object Identifier: doi:10.1214/EJP.v15-784
  
• [31] Peterson, J.: Strong transience of one-dimensional random walk in a random environment. Electron. C. Probab. 20 (2015), 1–10.
  Zentralblatt MATH: 1328.60229
  Digital Object Identifier: doi:10.1214/ECP.v20-4352
  
• [32] Peterson, J. and Seppäläinen T.: Current fluctuations of a system of one-dimensional random walks in random environment. Ann. Probab. 38 (2010), no. 6, 2258–2294.
  Zentralblatt MATH: 1210.60109
  Digital Object Identifier: doi:10.1214/10-AOP537
  Project Euclid: euclid.aop/1285334206
  
• [33] Peterson, J. and Zeitouni, O.: Quenched limits for transient, zero speed one-dimensional random walk in random environment. Ann. Probab. 37 (2009), no. 1, 143–188.
  Zentralblatt MATH: 1179.60070
  Digital Object Identifier: doi:10.1214/08-AOP399
  Project Euclid: euclid.aop/1234881687
  
• [34] Pólya, G.: Über eine Aufgabe der Wahrscheinlichkeitsrechnung betreffend die Irrfahrt im Straßennetz. Math. Ann. 84 (1921), 149–160.
• [35] Pólya, G.: Collected papers, Vol IV. Probability; combinatorics; teaching and learning in mathematics. Edited by Gian-Carlo Rota, M. C. Reynolds and R. M. Shortt. Mathematicians of Our Time, 22. MIT Press, Cambridge, MA, 1984. ix+642 pp.
• [36] Shi, Z. and Zindy, O.: A weakness in strong localization for Sinai’s walk. Ann. Probab. 35 (2007), no. 3, 1118–1140.
  Zentralblatt MATH: 1117.60091
  Digital Object Identifier: doi:10.1214/009117906000000863
  Project Euclid: euclid.aop/1178804324
  
• [37] Sinai, Ya. G.: The limiting behavior of a one-dimensional random walk in a random medium. Th. Probab. Appl. 27 (1982), 256–268.
  Zentralblatt MATH: 0505.60086
  
• [38] Solomon, F.: Random walks in a random environment. Ann. Probab. 3 (1975), 1–31.
  Zentralblatt MATH: 0305.60029
  Digital Object Identifier: doi:10.1214/aop/1176996444
  Project Euclid: euclid.aop/1176996444
  
• [39] Zeitouni, O.: Lecture notes on random walks in random environment. École d’été de probabilités de Saint-Flour 2001. Lecture Notes in Math. 1837 (2004), 189–312. Springer, Berlin.