Variance decay for functionals of the environment viewed by the particle
Variance decay for functionals of the environment viewed by the particle
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DOI：
10.1214/10-aihp375
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发表时间：
2009-02
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影响因子：
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通讯作者：
J. Mourrat
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文献类型：
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作者：
J. Mourrat
对于随机电导之间的随机游动，我们证明了粒子所看到的环境在方差意义下以多项式的速度收敛到平衡，我们的主要假设是电导有界于零。我们的方法的基础是建立一个Nash不等式，然后与简单的随机游动进行比较，或者通过基于鞅分解的更直接的分析。作为应用的一个例子，我们证明了在一定条件下，我们的结果隐含着游动的均方位移向其极限收敛的速度的估计。
For the random walk among random conductances, we prove that the environment viewed by the particle converges to equilibrium polynomially fast in the variance sense, our main hypothesis being that the conductances are bounded away from zero. The basis of our method is the establishment of a Nash inequality, followed either by a comparison with the simple random walk or by a more direct analysis based on a martingale decomposition. As an example of application, we show that under certain conditions, our results imply an estimate of the speed of convergence of the mean square displacement of the walk towards its limit.