Lecture series by Rami Atar

Professor Rami Atar (Technion-Israel Institute of Technology) will give a 5 hour lecture series 11-13 November 2025.

Title: Particle systems with boundary interactions and free boundary problems

Abstract:

A canonical example of a particle system with boundary interactions is the $N$-branching Brownian motion with spatial selection. In this model, $N$ Brownian particles on the real line move and branch independently, while a selection mechanism removes the leftmost particle at each branching event. Results of De Masi, Ferrari, Presutti, and Soprano-Loto (2017) and Berestycki, Brunet, and Penington (2019) show that its hydrodynamic scaling limit is described by a parabolic free boundary problem. A variety of related models have been introduced, motivated by the study of noisy traveling waves and by applications to population dynamics and load balancing in computer networks. After reviewing existing results and open questions concerning the connection between these models and free boundary problems, the talks will focus on a measure-theoretic free boundary formulation, and illustrate its use to analyze three specific models: diffusion with variable selection rate, the Atlas model, and density-dependent selection. Based in part on joint work with Amarjit Budhiraja, Leonid Mytnik and Gershon Wolansky.

This lecture series is in part supported by the ESPRC grant EP/W006227/1. Please email a.mjatovic@warwick.ac.uk if you would like to meet with the speaker during his visit at Warwick.