文章基本信息

标题：Regularity of biased 1D random walks in random environment
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作者：Alessandra Faggionato ; Michele Salvi
期刊名称：Latin American Journal of Probability and Mathematical Statistics
电子版ISSN：1980-0436
出版年度：2019
卷号：XVI
期号：2
页码：1213-1248
DOI：10.30757/ALEA.v16-46
出版社：Instituto Nacional De Matemática Pura E Aplicada
摘要：We study the asymptotic properties of nearest-neighbor random walksin 1d random environment under the influence of an external field of intensity 2 R. For ergodic shift-invariant environments, we show that the limiting velocityv() is always increasing and that it is everywhere analytic except at most in twopoints 􀀀 and +. When 􀀀 and + are distinct, v() might fail to be continuous.We refine the assumptions in Zeitouni (2004) for having a recentered CLT withdiffusivity 2() and give explicit conditions for 2() to be analytic. For therandom conductance model we show that, in contrast with the deterministic case,2() is not monotone on the positive (resp. negative) half-line and that it is notdifferentiable at = 0. For this model we also prove the Einstein Relation, both indiscrete and continuous time, extending the result of Lam and Depauw (2016).
关键词：Random walk in random environment; Asymptotic speed; Central;limit theorem; Random conductance model; Environment seen from the particle; Steady states;Einstein relation;