Year: 2025
Type: preprint
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.
Source: arXiv (Cornell University)
Authors: Caravenna, Francesco, Donadini, Anna
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4414741309
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