Directed Polymers in Markov Random Media

#### C. Boldrighini, R.A. Minlos, A. Pellegrinotti

2002, v.8, Issue 1, 81-105

ABSTRACT

We consider a model of directed polymers in discrete space and time assuming a Markov dependence of the environment in time. We extend results on the almost-sure validity of the Central Limit Theorem for small randomness in space dimension $\nu\geq 3$ which were previously obtained for independent environment by relying on two main technical tools: the analysis of the spectrum of a kind of transfer matrix which allows to treat the averaged model, and the explicit construction of a multiplicative orthonormal basis in the appropriate $L_2$ space, together with cluster estimates of cumulants of the basis functions.

Keywords: random walk,random media,Markov processes,Central Limit Theorem