Graph limits and random walks

Mini-WORKshop @ Benediktbeuern, September 13--16, 2020

Description

Random walks (RW) are one of the most fundamental stochastic processes which are amenable to detailed analysis. At the same time, RWs are at the core of numerous methods to extract information from complex systems. Furthermore, they occur as building blocks in many models of stochastic processes, such as interacting particle systems (IPS). Since many networks evolve in time, it is necessary to study RWs on evolving networks. In this workshop, we will focus on the models of RWs on evolving networks with the aim at both extending the existing theory of RWs themselves as well as developing tools for the study of IPS on evolving networks.

Keynote Talks

A series of four lectures. The titles are:

(1) Introduction to graphons.

(2) Large deviations for static graphons.

(3) Dynamic graphons.

(4) Sample-path large deviations for dynamic graphons.

[pdfs]

  • Perla Sousi (University of Cambridge): Random walk on dynamical percolation

We study the behaviour of random walk on dynamical percolation. In this model, the edges of a graph G are either open or closed and refresh their status at rate µ, while at the same time a random walker moves on G at rate 1, but only along edges which are open. I will talk about the mixing time of this process in the case where G is the d-dimensional lattice and the complete graph. I will also talk about comparison results for mixing and hitting times with the corresponding quantities for simple random walk on the underlying graph G, for general graphs. (Based on joint works with Y. Peres and J. Steif, with Sam Thomas and with Jonathan Hermon.)

Schedule


Sanitary/Hygienic Infosheet

All participants are requested to take note of the sanitary/hygienic infosheet (in German).

Venue

  • The guest house of the Benediktbeuern Monastery

  • Don-Bosco-Straße 1, 83671 Benediktbeuern, Germany