Mathematics – Probability
Scientific paper
2007-11-30
Annals of Probability 2009, Vol. 37, No. 1, 189-205
Mathematics
Probability
Published in at http://dx.doi.org/10.1214/08-AOP400 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of
Scientific paper
10.1214/08-AOP400
We consider random walk $(X_n)_{n\geq0}$ on $\mathbb{Z}^d$ in a space--time product environment $\omega\in\Omega$. We take the point of view of the particle and focus on the environment Markov chain $(T_{n,X_n}\omega)_{n\geq0}$ where $T$ denotes the shift on $\Omega$. Conditioned on the particle having asymptotic mean velocity equal to any given $\xi$, we show that the empirical process of the environment Markov chain converges to a stationary process $\mu_{\xi}^{\infty}$ under the averaged measure. When $d\geq3$ and $\xi$ is sufficiently close to the typical velocity, we prove that averaged and quenched large deviations are equivalent and when conditioned on the particle having asymptotic mean velocity $\xi$, the empirical process of the environment Markov chain converges to $\mu_{\xi}^{\infty}$ under the quenched measure as well. In this case, we show that $\mu_{\xi}^{\infty}$ is a stationary Markov process whose kernel is obtained from the original kernel by a Doob $h$-transform.
No associations
LandOfFree
Large deviations for random walk in a space--time product environment does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Large deviations for random walk in a space--time product environment, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Large deviations for random walk in a space--time product environment will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-702501