Law of large numbers for random walks on attractive spin-flip dynamics

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:127

Article

Bethuelsen, Stein Andreas¹  Heydenreich, Markus² 

[1] Tech Univ Munich, Fak Math, Boltzmannstr 3, D-85748 Garching, Germany

[2] Univ Munich, Math Inst, Theresienstr 39, D-80333 Munich, Germany

关键词: Random walks;    Dynamic random environments;    Strong law of large numbers;    Large deviation estimates;    Monotonicity;    Contact process;   

DOI  :  10.1016/j.spa.2016.09.016

来源: Elsevier

【 摘 要 】

We prove a law of large numbers for certain random walks on certain attractive dynamic random environments when initialised from all sites equal to the same state. This result applies to random walks on Z(d) with d >= 1. We further provide sufficient mixing conditions under which the assumption on the initial state can be relaxed, and obtain estimates on the large deviation behaviour of the random walk. As prime example we study the random walk on the contact process, for which we obtain a law of large numbers in arbitrary dimension. For this model, further properties about the speed are derived. (C) 2016 Elsevier B.V. All rights reserved.

【 授权许可】

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