Weak convergence of a random walk in a random environment
Copyright policy )Weak convergence of a random walk in a random environment
Let π i (x),i=1,...,d,x∈Z d , satisfy π i (x)≧α>0, and π1(x)+...+π d (x)=1. Define a Markov chain onZ d by specifying that a particle atx takes a jump of +1 in thei th direction with probability 1/2π i (x) and a jump of −1 in thei th direction with probability 1/2π i (x). If the π i (x) are chosen from a stationary, ergodic distribution, then for almost all π the corresponding chain converges weakly to a Brownian motion.
- Duke University United States
Monge-Ampere equation, ergodic distribution, Sums of independent random variables; random walks, 60F17, random environment, 60J15, Statistical mechanics of random media, disordered materials (including liquid crystals and spin glasses)
Monge-Ampere equation, ergodic distribution, Sums of independent random variables; random walks, 60F17, random environment, 60J15, Statistical mechanics of random media, disordered materials (including liquid crystals and spin glasses)
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