Simple analyticity criteria for repulsive multi-body potentials

2025/09/04 by Helmuth, Tyler, Pappik, Marcus, Perkins, Will
#FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Probability (math.PR)

paper · doi:10.48550/arxiv.2509.04287

Abstract

We prove a simple, explicit lower bound on the radius of a zero-free disk for Gibbs point processes defined by finite-range, repulsive multi-body interactions. Our lower bound improves on those previously known, and we demonstrate that it is essentially sharp in the generality with which our arguments apply. The key ingredient is a multi-body generalization of integral identities for point densities of Gibbs point processes in the spirit of earlier work of Michelen and Perkins.

Citations

• A Multi-Body Dobrushin-Sokal Criterion -- Part I
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• Exact General Solutions to Extraordinary N-body Problems