Hamiltonians on Random Walk Trajectories

Pablo A. Ferrari and Servet Mart\'{\i}nez

(PS file)

We consider Gibbs measures on the set of paths of nearest neighbors random walks on $Z_+$. The basic measure is the uniform measure on the set of paths of the simple random walk on $Z_+$ and the Hamiltonian awards each visit to site $x\in Z_+$ by an amount $\alpha_x\in R$, $x\in Z_+$. We give conditions on $(\alpha_x)$ that guarantee the existence of the (infinite volume) Gibbs measure. When comparing the measures in $Z_+$ with the corresponding measures in $Z$, the so called entropic repulsion appears as a counting effect.


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Last modified: Mon Sep 1 10:53:30 EST 1997