Alessandra Bianchi
Biography
Short bio
I studied Mathematics at the University of Bologna, and I obtained a PhD in Mathematics from the University of Roma Tre in 2007.
As a postdoc, I worked three years in the Weierstrass Institute of Berlin (WIAS) and three years in the Department of Mathematics of Bologna. I joined the Department of Mathematics of Padova in 2012, where I am associate professor in the area of Probability.
My research interests are Probability Theory and Statistical Mechanics. I have mainly focused my research on the analysis of Interacting particle systems, and on the characterization of mixing time and transition metastable times for Markovian dynamics.
I am also especially interested in the longtime behavior of random walks on random structures, and of more general stochastic dynamics evolving on random graphs.
Title: Mixing cutoff for simple random walks on the Chung-Lu directed graph
Abstract:
In this talk, we consider a simple random walk defined on a Chung-Lu directed graph, an inhomogeneous random network that extends the Erdos Renyi random digraph by including edges independently according to given Bernoulli laws, so that the average degrees are fixed. In this non-reversible setting, our focus is on the convergence toward the equilibrium of the dynamics.
In particular, under the assumption that the average degree grows logarithmically in the size n of the graph (weakly dense regime), we establish a cutoff phenomenon at the entropic time of order log(n)/loglog(n). Moreover, we prove that on a precise window, the cutoff profile converges to the Gaussian tail function. This is qualitatively similar to what was proved in a series of works by Bordenave, Caputo, Salez for the directed configuration model, where degrees are deterministically fixed. In terms of statistical ensembles, our analysis provides an extension of these cutoff results from a hard to a soft-constrained model.
