Meeting time of independent random walks in random environment

Christophe Gallesco

doi:10.1051/ps/2011159

All issues

Volume 17 (2013)

ESAIM: PS, 17 (2013) 257-292

References

Free Access

Issue		ESAIM: PS Volume 17, 2013


Page(s)		257 - 292
DOI		https://doi.org/10.1051/ps/2011159
Published online		08 February 2013

V. Belitsky, P. Ferrari, M. Menshikov and S. Popov, A mixture of the exclusion process and the voter model. Bernoulli 7 (2001) 119–144. [CrossRef] [MathSciNet] [Google Scholar]
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F. Comets and S.Yu. Popov, Limit law for transition probabilities and moderate deviations for Sinai’s random walk in random environment. Probab. Theory Relat. Fields 126 (2003) 571–609. [CrossRef] [Google Scholar]
F. Comets and S.Yu. Popov, A note on quenched moderate deviations for Sinai’s random walk in random environment. ESAIM : PS 8 (2004) 56–65. [CrossRef] [EDP Sciences] [Google Scholar]
F. Comets, M.V. Menshikov and S.Yu. Popov, Lyapunov functions for random walks and strings in random environment. Ann. Probab. 26 (1998) 1433–1445. [CrossRef] [MathSciNet] [Google Scholar]
A. Dembo, N. Gantert, Y. Peres and Z. Shi, Valleys and the maximal local time for random walk in random environment. Probab. Theory Relat. Fields 137 (2007) 443–473. [CrossRef] [Google Scholar]
N. Enriquez, C. Sabot and O. Zindy, Aging and quenched localization one-dimensional random walks in random environment in the bub-ballistic regime. Bulletin de la S.M.F. 137 (2009) 423–452. [Google Scholar]
A. Fribergh, N. Gantert and S.Yu. Popov, On slowdown and speedup of transient random walks in random environment. Probab. Theory Relat. Fields 147 (2010) 43–88. [CrossRef] [Google Scholar]
C. Gallesco, On the moments of the meeting time of independent random walks in random environment. arXiv:0903.4697 (2009). [Google Scholar]
N. Gantert, Y. Peres and Z. Shi, The infinite valley for a recurrent random walk in random environment. Ann. Inst. Henri Poincaré 46 (2010) 525–536. [CrossRef] [MathSciNet] [Google Scholar]
A. Greven and F. den Hollander, Large deviations for a random walk in random environment. Ann. Probab. 22 (1994) 1381 − 1428. [CrossRef] [MathSciNet] [Google Scholar]
Y. Hu and Z. Shi, Moderate deviations for diffusions with Brownian potentials. Ann. Probab. 32 (2004) 3191–3220. [CrossRef] [MathSciNet] [Google Scholar]
B. Hughes, Random Walks and Random Environments. The Clarendon Press, Oxford University Press, New York. Random Environments 2 (1996). [Google Scholar]
H. Kesten, M.V.Kozlov and F. Spitzer, A limit law for random walk in a random environment. Compos. Math. 30 (1975) 145–168. [Google Scholar]
J. Komlós, P. Major and G. Tusnády, An approximation of partial sums of independent RV’s and the sample DF. I. Z. Wahrscheinlichkeitstheor. Verw. Gebiete 32 (1975) 111–131. [Google Scholar]
L. Saloff-Coste, Lectures on Finite Markov Chains. Lectures on probability theory and statistics, Saint-Flour, 1996, Springer, Berlin. Lect. Notes Math. 1665 (1997) 301–413. [CrossRef] [Google Scholar]
Z. Shi, Sinai’s Walk via Stochastic Calculus, in Milieux Aléatoires Panoramas et Synthèses 12, edited by F. Comets and E. Pardoux. Société Mathématique de France, Paris (2001). [Google Scholar]
Ya.G. Sinai, The limiting behavior of one-dimensional random walk in random medium. Theory Probab. Appl. 27 (1982) 256–268. [Google Scholar]
F. Solomon, Random walks in a random environment. Ann. Probab. 3 (1975) 1–31. [CrossRef] [Google Scholar]
O. Zeitouni, Lecture Notes on Random Walks in Random Environment given at the 31st Probability Summer School in Saint-Flour, Springer. Lect. Notes Math. 1837 (2004) 191–312. [Google Scholar]

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[1] V. Belitsky, P. Ferrari, M. Menshikov and S. Popov, A mixture of the exclusion process and the voter model. Bernoulli 7 (2001) 119–144. [CrossRef] [MathSciNet] [Google Scholar]

[2] W. Böhm and S.G. Mohanty, On the Karlin–McGregor theorem and applications. Ann. Appl. Probab. 7 (1997) 314–325. [CrossRef] [Google Scholar]

[3] F. Comets and S.Yu. Popov, Limit law for transition probabilities and moderate deviations for Sinai’s random walk in random environment. Probab. Theory Relat. Fields 126 (2003) 571–609. [CrossRef] [Google Scholar]

[4] F. Comets and S.Yu. Popov, A note on quenched moderate deviations for Sinai’s random walk in random environment. ESAIM : PS 8 (2004) 56–65. [CrossRef] [EDP Sciences] [Google Scholar]

[5] F. Comets, M.V. Menshikov and S.Yu. Popov, Lyapunov functions for random walks and strings in random environment. Ann. Probab. 26 (1998) 1433–1445. [CrossRef] [MathSciNet] [Google Scholar]

[6] A. Dembo, N. Gantert, Y. Peres and Z. Shi, Valleys and the maximal local time for random walk in random environment. Probab. Theory Relat. Fields 137 (2007) 443–473. [CrossRef] [Google Scholar]

[7] N. Enriquez, C. Sabot and O. Zindy, Aging and quenched localization one-dimensional random walks in random environment in the bub-ballistic regime. Bulletin de la S.M.F. 137 (2009) 423–452. [Google Scholar]

[8] A. Fribergh, N. Gantert and S.Yu. Popov, On slowdown and speedup of transient random walks in random environment. Probab. Theory Relat. Fields 147 (2010) 43–88. [CrossRef] [Google Scholar]

[9] C. Gallesco, On the moments of the meeting time of independent random walks in random environment. arXiv:0903.4697 (2009). [Google Scholar]

[10] N. Gantert, Y. Peres and Z. Shi, The infinite valley for a recurrent random walk in random environment. Ann. Inst. Henri Poincaré 46 (2010) 525–536. [CrossRef] [MathSciNet] [Google Scholar]

[11] A. Greven and F. den Hollander, Large deviations for a random walk in random environment. Ann. Probab. 22 (1994) 1381 − 1428. [CrossRef] [MathSciNet] [Google Scholar]

[12] Y. Hu and Z. Shi, Moderate deviations for diffusions with Brownian potentials. Ann. Probab. 32 (2004) 3191–3220. [CrossRef] [MathSciNet] [Google Scholar]

[13] B. Hughes, Random Walks and Random Environments. The Clarendon Press, Oxford University Press, New York. Random Environments 2 (1996). [Google Scholar]

[14] H. Kesten, M.V.Kozlov and F. Spitzer, A limit law for random walk in a random environment. Compos. Math. 30 (1975) 145–168. [Google Scholar]

[15] J. Komlós, P. Major and G. Tusnády, An approximation of partial sums of independent RV’s and the sample DF. I. Z. Wahrscheinlichkeitstheor. Verw. Gebiete 32 (1975) 111–131. [Google Scholar]

[16] L. Saloff-Coste, Lectures on Finite Markov Chains. Lectures on probability theory and statistics, Saint-Flour, 1996, Springer, Berlin. Lect. Notes Math. 1665 (1997) 301–413. [CrossRef] [Google Scholar]

[17] Z. Shi, Sinai’s Walk via Stochastic Calculus, in Milieux Aléatoires Panoramas et Synthèses 12, edited by F. Comets and E. Pardoux. Société Mathématique de France, Paris (2001). [Google Scholar]

[18] Ya.G. Sinai, The limiting behavior of one-dimensional random walk in random medium. Theory Probab. Appl. 27 (1982) 256–268. [Google Scholar]

[19] F. Solomon, Random walks in a random environment. Ann. Probab. 3 (1975) 1–31. [CrossRef] [Google Scholar]

[20] O. Zeitouni, Lecture Notes on Random Walks in Random Environment given at the 31st Probability Summer School in Saint-Flour, Springer. Lect. Notes Math. 1837 (2004) 191–312. [Google Scholar]