30/10/2024, 16:00 — 17:00 — Online
Matteo Quattropani, University of Roma (Tor Vergata)
Cutoff at the entropic time for Repeated Block Averages
The Averaging process (a.k.a. repeated averages) is a redistribution model over the vertex set of a graph. Given a graph G, the process starts with a non-negative mass associated to each vertex. At each discrete time an edge is sampled uniformly at random, and the masses at the two extremes of the edge are equally redistributed on these two vertices. Clearly, as time grows to infinity, the state of the system will converge (in some sense) to a flat configuration in which all the vertices have the same mass. Despite the simplicity of its formulation, even in the case of seemingly straightforward geometries—such as the complete graph or the 1-d torus— the analysis of the mixing behavior of this process can be handled only by means of non trivial probabilistic and functional analytic techniques. In the talk I will focus on the (mean-field) hypergraph case, in which edges are replaced by a more general notion of “blocks”. I will discuss the speed of convergence to equilibrium as a function of the blocks size, providing sharp conditions for the emergence of the cutoff phenomenon, i.e., a dynamical phase transition in which equilibrium is reached abruptly on a given time scale.
The talk is based on joint works with Pietro Caputo (Roma) and Federico Sau (Trieste).
Note the different time for the winter seminars: 4pm instead of 5pm (Portugal time).
See also here: https://spmes.impa.br/
