A quenched invariance principle for non-elliptic random walk in i.i.d. balanced random environment

作者：Berger Noam; Deuschel Jean Dominique^*

来源：Probability Theory and Related Fields, 2014, 158(1-2): 91-126.

DOI：10.1007/s00440-012-0478-4

• Random walks in random environments
• Non-ellipticity
• Maximum principle
• Mean value inequality
• Percolation

We consider a random walk on , in an i.i.d. balanced random environment, that is a random walk for which the probability to jump from to nearest neighbor is the same as to nearest neighbor . Assuming that the environment is genuinely -dimensional and balanced we show a quenched invariance principle: for almost every environment, the diffusively rescaled random walk converges to a Brownian motion with deterministic non-degenerate diffusion matrix. Within the i.i.d. setting, our result extend both Lawler%26apos;s uniformly elliptic result (Comm Math Phys, 87(1), pp 81-87, 1982/1983) and Guo and Zeitouni%26apos;s elliptic result (to appear in PTRF, 2010) to the general (non elliptic) case. Our proof is based on analytic methods and percolation arguments.

• 出版日期2014-2