# Entropic repulsion of the lattice free field

Bolthausen, E; Deuschel, J-D; Zeitouni, O (1995). Entropic repulsion of the lattice free field. Communications in Mathematical Physics, 170(2):417-443.

## Abstract

Consider the massless free field on the d-dimensional lattice ℤ d , d≥3; that is the centered Gaussian field on ℝ ℤ d with covariances given by the Green function of the simple random walk on ℤ d . We show that the probability, that all the spins are positive in a box of volume N d , decays exponentially at a rate of order N d-2 logN and compute explicitly the corresponding constant in terms of the capacity of the unit cube. The result is extended to a class of transient random walks with transition functions in the domain of the normal and α-stable law.

## Abstract

Consider the massless free field on the d-dimensional lattice ℤ d , d≥3; that is the centered Gaussian field on ℝ ℤ d with covariances given by the Green function of the simple random walk on ℤ d . We show that the probability, that all the spins are positive in a box of volume N d , decays exponentially at a rate of order N d-2 logN and compute explicitly the corresponding constant in terms of the capacity of the unit cube. The result is extended to a class of transient random walks with transition functions in the domain of the normal and α-stable law.

## Statistics

### Citations

Dimensions.ai Metrics
43 citations in Web of Science®
43 citations in Scopus®