arXiv subjects

Rogério Gomes Alves

Publications and source records attributed to Rogério Gomes Alves.

2 recordsLinked to original sources

arXiv2017

On Kirkwood-Salsburg solutions at criticality

In this work we study the Kirkwood-Salsburg equations of equilibrium classical continuous systems. We prove a Laurent expansion for the resolvent, at an eigenvalue of largest modulus of the Kirkwood-Salsburg operator, which is shown to have a pole of order 1. Then we prove that all correlation functions have an asymptotic limit as the activity parameter tends to a smallest zero of the partition function. As corollary, we show that any smallest zero of the partition function is simple. The main consequence is that in case of positive or hardcore potentials we find the spectral radius of the Kirkwood-Salsburg operator and the convergence radius of the solutions.

math-ph↗

arXiv2013

Witness trees in the Moser-Tardos algorithmic Lovász Local Lemma and Penrose trees in the hard core lattice gas

We point out a close connection between the Moser-Tardos algorithmic version of the Lovász Local Lemma, a central tool in probabilistic combinatorics, and the cluster expansion of the hard core lattice gas in statistical mechanics. We show that the notion of witness trees given by Moser and Tardos is essentially coincident with that of Penrose trees in the Cluster expansion scheme of the hard core gas. Such an identification implies that the Moser Tardos algorithm is successful in a polynomial time if the Cluster expansion converges.

math-ph↗