Construction of a Gibbs measure for the zonal Dirac equation
Analysis of PDEs
2026-01-21 v1 Probability
Abstract
We propose a framework to construct Gibbs measures for the Dirac equation. We consider the Dirac equation on the sphere with a "Hartree-type" nonlinearity. We consider a zonal model, that is the analog of a spherically symmetric model but on the sphere. We build a Gibbs measure for this model. With a compactness argument, we prove the existence of a random variable that is a weak solution to the Dirac equation and whose law is the Gibbs measure at all times.
Keywords
Cite
@article{arxiv.2601.11730,
title = {Construction of a Gibbs measure for the zonal Dirac equation},
author = {Anne-Sophie de Suzzoni and Cyril Malézé},
journal= {arXiv preprint arXiv:2601.11730},
year = {2026}
}
Comments
28p