Sunder Sethuraman is a Professor of Mathematics at the University of Arizona. Before arriving in Tucson in 2011, he was at Iowa State University for a number of years. He received his PhD from Courant Institute, NYU, in 1995. Much of his research has been on aspects of stochastic interacting particle systems, such as scaling limits which connect different types of particle level behaviors to their associated continuum laws. In 2008, he received the best paper prize from Ann. IHP Prob. Stat., and in 2018 was a Simons and JSPS Fellow. He also became a Fellow of the IMS in 2018.

This IMS–Bernoulli Society Schramm lecture will be delivered at the 44th Stochastic Processes and their Applications conference (SPA2025) in Wrocław, Poland, July 14–18, 2025: https://spa.pwr.edu.pl/

On the derivation of mean-curvature flow and its fluctuations from microscopic interactions

The emergence of mean-curvature flow of an interface between different phases or populations is a phenomenon of long standing interest in statistical physics. In this talk, we review recent progress with respect to a class of reaction-diffusion stochastic particle systems on an n-dimensional lattice. In such a process, particles can move across sites as well as be created or annihilated according to diffusion and reaction rates. These rates will be chosen so that there are two preferred particle mass density levels a₁, a₂.

In the evolution, one may understand, when the diffusion and reaction schemes are appropriately scaled, that a rough interface forms between the regions where the mass density is close to a₁ or a₂. Via notions in the theory of hydrodynamic limits, we discuss when the scaled limit of the particle mass density field in n ≥ 2 is a sharp interface flow by mean-curvature.

We also discuss the fluctuation field limit of the mass near the forming interface, which informs on the approach to the continuum view in a certain stationary regime in n = 1, 2.