Positive temperature versions of two theorems on first-passage percolation

TL;DR

This paper extends key fluctuation bounds from first-passage percolation to the positive-temperature setting of random Schrödinger operators, providing new insights into their probabilistic behavior.

Contribution

It transposes two fundamental theorems from first-passage percolation to the positive-temperature context of random Schrödinger operators, a novel adaptation.

Findings

Tail bound for fluctuations established

Sublinear variance bound adapted to positive temperature

Enhanced understanding of probabilistic estimates in quantum models

Abstract

The estimates on the fluctuations of first-passsage percolation due to Talagrand (a tail bound) and Benjamini--Kalai--Schramm (a sublinear variance bound) are transcribed into the positive-temperature setting of random Schroedinger operators.