Enhanced noise sensitivity, 2D directed polymers and Stochastic Heat Flow

TL;DR

This paper extends noise sensitivity analysis to general random variables, applies it to 2D directed polymers, and shows the asymptotic independence of the Stochastic Heat Flow from the underlying noise.

Contribution

It introduces an enhanced noise sensitivity framework and applies it to critical 2D directed polymers, establishing their asymptotic independence from disorder noise.

Findings

Enhanced noise sensitivity for 2D directed polymers at criticality

Proved asymptotic independence of the Stochastic Heat Flow from white noise

Derived optimal bounds for noise sensitivity in general settings

Abstract

We investigate noise sensitivity beyond the classical setting of binary random variables, extending the celebrated result by Benjamini, Kalai, and Schramm to a wide class of functions of general random variables. Our approach yields improved bounds with optimal rates. We also consider an enhanced form of noise sensitivity which yields asymptotic independence, rather than mere decorrelation. We apply these result to establish enhanced noise sensitivity for the partition functions of 2D directed polymers, in the critical regime where they converge to the critical 2D Stochastic Heat Flow. As a consequence, we prove that the Stochastic Heat Flow is independent of the white noise arising from the disorder.