In this talk, we present an overview of some quantitative aspects of convergence to equilibrium for a class of interacting particle systems that we refer to as Stochastic Exchange Models (SEM). In these models, particles interact via binary updates, exchanging
a conserved quantity that can be interpreted as mass, energy, or momentum. Examples in this class include, among others, Kac’s walk, the Kipnis–Marchioro–Presutti model, and the Averaging process.
Although these processes are Markovian, many standard techniques for analyzing finite-state Markov chains are not directly applicable due to the continuum nature of the configuration space, the presence of conservation laws, or singular constraints. We will
provide an overview of the models in this class, with particular emphasis on spectral gaps and mixing times.
The talk is based on a series of joint works with Pietro Caputo (Rome) and Seonwoo Kim (Seoul).
Meeting ID: 92945513591
Passcode: 131676