Non-Uniqueness of Gibbs measures relative to Brownian motion
Volker Betz, Olaf Wittich
TL;DR
This paper investigates Gibbs measures related to Brownian motion with Feynman-Kac potentials, demonstrating that for many potentials, including Coulomb, there are infinitely many such measures in the infinite volume limit.
Contribution
It establishes the existence of infinitely many Gibbs measures for a broad class of potentials, highlighting non-uniqueness phenomena in this context.
Findings
Existence of infinitely many Gibbs measures for Coulomb potential
Non-uniqueness of Gibbs measures in the Feynman-Kac setting
Applicable to a large class of potentials including Coulomb
Abstract
We consider Gibbs measures relative to Brownian motion of Feynman-Kac type, with single site potential V. We show that for a large class of V, including the Coulomb potential, there exist infinitely many infinite volume Gibbs measures.
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Taxonomy
TopicsStochastic processes and statistical mechanics · Markov Chains and Monte Carlo Methods · Stochastic processes and financial applications