The concentration inequality for a discrete height function model perturbed by random potential

TL;DR

This paper proves a concentration inequality for a discrete height function model with a perturbed random potential, showing the robustness of the annealing method in such probabilistic models.

Contribution

It introduces a novel proof of concentration inequality for models with additive random potential perturbations, extending existing methods.

Findings

Proves concentration inequality for perturbed height function models

Demonstrates robustness of annealing-based proof methods

Extends applicability of concentration results to perturbed systems

Abstract

We present a proof of the concentration inequality for a discrete random surface model, where the underlying potential is perturbed by an additive random potential. The proof is based on annealing the random potential, and follows the method of [CEP96] and other works. Our result demonstrates the robustness of this method.