Dear colleagues,

We are happy to announce the following online talk:

Speaker: *Michele Salvi* (Università di Roma "Tor Vergata")

Title: *Scale-free percolation mixing time.*

Abstract: Scale-free percolation is a spatial inhomogeneous random graph model which features three fundamental properties that are often present in real-world networks: (1) Scale-free: the degree of the nodes follows a power law; (2) Small-world: two far-away nodes have typically a small graph distance; (3) Positive clustering coefficient: two nodes with a common neighbour have a good chance to be linked. We study the mixing time of the simple random walk on this structure in one dimension and depict a rich phase diagram in the parameters of the model. In particular, we prove that the presence of hubs can speed up the mixing of the chain. Joint work with Alessandra Cipriani (UCL).

*Date and time:* Monday May 9, 17:30-18:30 (Rome time zone)

*Zoom link:* https://us02web.zoom.us/j/6815552946

This talk is part of the *(PMS)^2*: *Pavia-Milano Seminar series on Probability and Mathematical Statistics* organized jointly by the universities Milano-Bicocca, Pavia, Milano-Politecnico and Milano-Statale.

Participation is free and welcome!

Best regards The organizers (Mario Maurelli, Carlo Orrieri, Maurizia Rossi, Margherita Zanella)