KPZ-type fluctuation exponents for interacting diffusions in equilibrium

TL;DR

This paper investigates the fluctuation behavior of interacting diffusions in equilibrium, demonstrating KPZ-type $N^{2/3}$ variance scaling for a broad class of potentials without relying on integrability.

Contribution

It extends KPZ fluctuation results to non-integrable interacting diffusion models with general convex potentials using analytic, non-perturbative methods.

Findings

Variance of height function scales as $N^{2/3}$

Matching upper and lower bounds established for fluctuations

Results apply to non-integrable models in the KPZ universality class

Abstract

We consider systems of $N$ diffusions in equilibrium interacting through a potential $V$. We study a "height function" which for the special choice $V(x) = \e^{-x}$, coincides with the partition function of a stationary semidiscrete polymer, also known as the (stationary) O'Connell-Yor polymer. For a general class of smooth convex potentials (generalizing the O'Connell-Yor case), we obtain the order of fluctuations of the height function by proving matching upper and lower bounds for the variance of order $N^{2/3}$, the expected scaling for models lying in the KPZ universality class. The models we study are not expected to be integrable and our methods are analytic and non-perturbative, making no use of explicit formulas or any results for the O'Connell-Yor polymer.