Pablo A. Ferrari, Servet Martinez
Hamiltonians on random walk trajectories
(271K, ps)

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.