TY - JOUR

T1 - A quenched invariance principle for non-elliptic random walk in i.i.d. balanced random environment

AU - Berger, Noam

AU - Deuschel, Jean Dominique

N1 - Funding Information:
The research was partially supported by grant 2006477 of the Israel-U.S. binational science foundation, by grant 152/2007 of the German Israeli foundation and by ERC StG grant 239990.

PY - 2014/2

Y1 - 2014/2

N2 - We consider a random walk on ℤd, d ≥ 2, in an i.i.d. balanced random environment, that is a random walk for which the probability to jump from x ∈ ℤd to nearest neighbor x+e is the same as to nearest neighbor x-e. Assuming that the environment is genuinely d-dimensional and balanced we show a quenched invariance principle: for P 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's uniformly elliptic result (Comm Math Phys, 87(1), pp 81-87, 1982/1983) and Guo and Zeitouni's elliptic result (to appear in PTRF, 2010) to the general (non elliptic) case. Our proof is based on analytic methods and percolation arguments.

AB - We consider a random walk on ℤd, d ≥ 2, in an i.i.d. balanced random environment, that is a random walk for which the probability to jump from x ∈ ℤd to nearest neighbor x+e is the same as to nearest neighbor x-e. Assuming that the environment is genuinely d-dimensional and balanced we show a quenched invariance principle: for P 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's uniformly elliptic result (Comm Math Phys, 87(1), pp 81-87, 1982/1983) and Guo and Zeitouni's elliptic result (to appear in PTRF, 2010) to the general (non elliptic) case. Our proof is based on analytic methods and percolation arguments.

KW - Maximum principle

KW - Mean value inequality

KW - Non-ellipticity

KW - Percolation

KW - Random walks in random environments

UR - http://www.scopus.com/inward/record.url?scp=84892878760&partnerID=8YFLogxK

U2 - 10.1007/s00440-012-0478-4

DO - 10.1007/s00440-012-0478-4

M3 - Article

AN - SCOPUS:84892878760

SN - 0178-8051

VL - 158

SP - 91

EP - 126

JO - Probability Theory and Related Fields

JF - Probability Theory and Related Fields

IS - 1-2

ER -