Limits of graphs and L^2 operators – Ágnes Backhausz, Balázs Szegedy

Ágnes Backhausz
Eötvös Loránd University, Hungary
https://backhauszagi.web.elte.hu/

Date(s) : 08/02/2019   iCal
11 h 00 min - 12 h 00 min

The goal of the talk is to give an overview on graph limit theory, its applications to the spectral theory of random graphs, and, as a recent development, its extension to operators acting on L^2 spaces.

In the last 10-15 years, it was demonstrated that a limiting view on graphs can also provide a new approach to various problems in probability theory. A major difficulty in graph limit theory is that it is a rather diverse subject; different notions have been used
for sparse and dense graph sequences. In a recent paper, we proposed the notion of action convergence of operators acting on L^2 spaces, which unifies dense graph convergence and local-global convergence of bounded degree graphs. We give an introduction to action convergence, and explain how it is related to random graphs and matrices.

https://www.cambridge.org/core/journals/canadian-journal-of-mathematics/article/action-convergence-of-operators-and-graphs/

Balázs Szegedy website

 

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