May 2023 KPZ-type fluctuation exponents for interacting diffusions in equilibrium
Benjamin Landon, Christian Noack, Philippe Sosoe
Author Affiliations +
Ann. Probab. 51(3): 1139-1191 (May 2023). DOI: 10.1214/22-AOP1617


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)=ex, 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 N2/3, 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 nonperturbative, making no use of explicit formulas or any results for the O’Connell–Yor polymer.

Funding Statement

The work of B.L. is partially supported by an NSERC Discovery grant.
The work of P.S. is partially supported by NSF Grants DMS-1811093 and DMS-2154090.


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Benjamin Landon. Christian Noack. Philippe Sosoe. "KPZ-type fluctuation exponents for interacting diffusions in equilibrium." Ann. Probab. 51 (3) 1139 - 1191, May 2023.


Received: 1 June 2022; Revised: 1 October 2022; Published: May 2023
First available in Project Euclid: 2 May 2023

MathSciNet: MR4583065
zbMATH: 1517.82047
Digital Object Identifier: 10.1214/22-AOP1617

Primary: 82D60
Secondary: 60H10

Keywords: Diffusions , KPZ universality

Rights: Copyright © 2023 Institute of Mathematical Statistics


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Vol.51 • No. 3 • May 2023
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