KPZ-type fluctuation exponents for interacting diffusions in equilibrium
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) = -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 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 non-perturbative, making no use of explicit formulas or any results for the O'Connell-Yor polymer.