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Article Dans Une Revue ALEA : Latin American Journal of Probability and Mathematical Statistics Année : 2019

REGULARITY OF BIASED 1D RANDOM WALKS IN RANDOM ENVIRONMENT

Résumé

We study the asymptotic properties of nearest-neighbor random walks in 1d random environment under the influence of an external field of intensity λ ∈ R. For ergodic shift-invariant environments, we show that the limiting velocity v(λ) is always increasing and that it is everywhere analytic except at most in two points λ− and λ+. When λ− and λ+ are distinct, v(λ) might fail to be continuous. We refine the assumptions in [?] for having a recentered CLT with diffusivity σ 2 (λ) and give explicit conditions for σ 2 (λ) to be analytic. For the random conductance model we show that, in contrast with the deterministic case, σ 2 (λ) is not monotone on the positive (resp. negative) half-line and that it is not differentiable at λ = 0. For this model we also prove the Einstein Relation, both in discrete and continuous time, extending the result of Lam and Depaw (2016).
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Dates et versions

hal-02374577 , version 1 (21-11-2019)

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Alessandra Faggionato, Michele Salvi. REGULARITY OF BIASED 1D RANDOM WALKS IN RANDOM ENVIRONMENT. ALEA : Latin American Journal of Probability and Mathematical Statistics, 2019, 16 (2), pp.1213. ⟨10.30757/ALEA.v16-46⟩. ⟨hal-02374577⟩
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