A Concentration of Measure Phenomenon in Lattice Yang-Mills

TL;DR

This paper shows that the distribution of lattice Yang-Mills measures becomes Gaussian in the limit, providing a new perspective on the measure's behavior and connecting it to the strong-coupling expansion.

Contribution

It introduces a concentration of measure phenomenon for lattice Yang-Mills, linking measure concentration to the strong-coupling expansion.

Findings

Measure concentrates as a Gaussian

Connection to strong-coupling expansion

Provides a new analytical perspective

Abstract

We demonstrate that the pushforward of the product of Haar measures by the lattice Yang-Mills action concentrates as a Gaussian. It is also sketched how, using this fact, one can recover the strong-coupling expansion.