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Graph limits and spectral theory

Date: Thursday, May 16, 2019 16:00 - 17:00
Speaker: Agnes Backhausz (Eotvos Lorand University and Renyi Institute)
Location: Big Seminar room Ground floor / Office Bldg West (I21.EG.101)
Series: Mathematics and CS Seminar
Host: Laszlo Erdös
Contact: PETZ Caroline
Lab building west seminar room


The goal of the talk is to give an overview on the basic notions of graph limit theory, and to present recent results about its applications to the spectral theory of random graphs and random matrices. By identifying continuous limit objects (e.g. L^2 operators) as the limit of convergent graph sequences, graph limit theory is a powerful combination of tools from analysis, combinatorics and probability theory. In the first part of the talk, we summarize the notions of local limit of bounded degree graphs, the limit of dense graph sequences, and the recently defined notion of action convergence, which works for graphs of intermediate density as well. Then we present two applications on the empirical distribution of eigenvectors of random regular graphs and random sign matrices.
Joint work with Balzs Szegedy.
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