Central limit theorem for random walks in doubly stochastic random environment: ${\mathscr{H}_{-1}}$ suffices
Central limit theorem for random walks in doubly stochastic random environment: ${\mathscr{H}_{-1}}$ suffices
复制标题
双随机环境中随机游走的中心极限定理： ${mathscr{H}_{-1}}$ 足够
DOI：
10.1214/16-aop1166
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发表时间：
2017
影响因子：
2.3
通讯作者：
B. Tóth
中科院分区：
文献类型：
--
作者：
G. Kozma;B. Tóth
在施加于漂移场的H−1H−1-条件下，证明了平稳遍历双随机环境中ZDZD上随机游动的位移在扩散尺度下的中心极限定理.该条件等价于假定漂移场的流张量是平稳的平方可积的。这改进了现有的最佳结果[马尔可夫过程中的波动-时间对称性和鞅近似(2012年)Springer]，其中假定流张量是Lmax{2+δ，d}Lmax{2+δ，d}，其中δ>；0δ>；0。我们的证明依赖于[Bull]的宽松部门条件的延伸。安装数学课。阿卡德。罪孽。(N.S.)7(2012)463-476]，并且技术上比Oelschlager[Ann]类似结果的现有早期证明要简单得多。可能吧。16(1988)1084-1126]和Komorowski，Landim and Olla[马尔可夫过程中的波动-时间对称性和鞅近似(2012)Springer]。
We prove a central limit theorem under diffusive scaling for the displacement of a random walk on ZdZd in stationary and ergodic doubly stochastic random environment, under the H−1H−1-condition imposed on the drift field. The condition is equivalent to assuming that the stream tensor of the drift field be stationary and square integrable. This improves the best existing result [Fluctuations in Markov Processes—Time Symmetry and Martingale Approximation (2012) Springer], where it is assumed that the stream tensor is in Lmax{2+δ,d}Lmax{2+δ,d}, with δ>0δ>0. Our proof relies on an extension of the relaxed sector condition of [Bull. Inst. Math. Acad. Sin. (N.S.) 7 (2012) 463–476], and is technically rather simpler than existing earlier proofs of similar results by Oelschlager [Ann. Probab. 16 (1988) 1084–1126] and Komorowski, Landim and Olla [Fluctuations in Markov Processes—Time Symmetry and Martingale Approximation (2012) Springer].