论文标题
从西那奈（Sinaï）步行中看到的环境的极限
Limit of the environment viewed from Sinaï's walk
论文作者
论文摘要
对于Sinaï的步行（X_K），我们表明，从粒子（\ bar \ w_k）中看到的环境的经验度量在法律上收敛到某种随机度量S。此极限度量是根据Infinite Valley明确给出的，Infinite Valley的结构又回到Golosov。结果，“法律” ergodic定理具有（\ bar \ w_k）的加性功能。当此“法律”的限制是确定性的，它的可能性就存在。这允许对弹道“环境方法”的复发情况进行一些扩展，可追溯到Kozlov和Molchanov。特别是，我们显示了一个lln和一个混合CLT，用于总和sum_ {k = 1}^nf（Δx_k），其中f有界限并取决于步骤ΔX_K：= x__ {k+1} -x_k。
For Sinaï's walk (X_k) we show that the empirical measure of the environment seen from the particle (\bar\w_k) converges in law to some random measure S. This limit measure is explicitly given in terms of the infinite valley, which construction goes back to Golosov. As a consequence an "in law" ergodic theorem holds for additive functionals of (\bar\w_k) . When the limit in this "in law" ergodic theorem is deterministic, it holds in probability. This allows some extensions to the recurrent case of the ballistic "environment's method" dating back to Kozlov and Molchanov. In particular, we show an LLN and a mixed CLT for the sums sum_{k=1}^nf(ΔX_k), where f is bounded and depending on the steps ΔX_k:=X_{k+1}-X_k.
