97-465 Pablo A. Ferrari, Servet Martinez

Hamiltonians on random walk trajectories (271K, ps) Sep 1, 97

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Abstract. 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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