Remarks on superconcentration and Gamma calculus. Application to Spin Glasses

TL;DR

This paper explores superconcentration in spin glasses, demonstrating how Gamma calculus can bound variance of functions under curvature conditions, with applications to free energy models.

Contribution

It introduces a novel application of Bakry-Emery's Gamma calculus to bound variances in spin glass models, linking curvature criteria to superconcentration phenomena.

Findings

Gamma calculus provides effective variance bounds

Application to free energy in spin glasses

Establishes links between curvature and superconcentration

Abstract

This note is concerned with the so-called superconcentration phenomenon. It shows that the Bakry-Emery's Gamma calculus can provide relevant bound on the variance of function satisfying a inverse, integrated, curvature criterion. As an illustration, we present some variance bounds for the Free Energy in different models from Spin Glasses Theory.