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October 1998 Lyapounov exponents and quenched large deviations for multidimensional random walk in random environment
Martin P. W. Zerner
Ann. Probab. 26(4): 1446-1476 (October 1998). DOI: 10.1214/aop/1022855870

Abstract

Assign to the lattice sizes $z \epsilon \mathbb{Z}^d$ i.i.d. random 2 $d$-dimensional vectors $(\omega(z, z + e))_{|e|=1}$ whose entries take values in the open unit interval and add up to one. Given a realization $\omega$ of this environment, let $(X_n)_{n \geq o}$ be a Markov chain on $\mathbb{Z}^d$ which, when at $z$, moves one step to its neighbor $z + e$ with transition probability $\omega(z, z + e)$. We derive a large deviation principle for $X_n/n$ by means of a result similar to the shape theorem of first-passage percolation and related models. This result produces certain constants that are the analogue of the Lyapounov exponents known from Brownian motion in Poissonian potential or random walk in random potential. We follow a strategy similar to Sznitman.

Citation

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Martin P. W. Zerner. "Lyapounov exponents and quenched large deviations for multidimensional random walk in random environment." Ann. Probab. 26 (4) 1446 - 1476, October 1998. https://doi.org/10.1214/aop/1022855870

Information

Published: October 1998
First available in Project Euclid: 31 May 2002

zbMATH: 0937.60095
MathSciNet: MR1675027
Digital Object Identifier: 10.1214/aop/1022855870

Subjects:
Primary: 60F10, 82C41

Rights: Copyright © 1998 Institute of Mathematical Statistics

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Vol.26 • No. 4 • October 1998
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