Limits of kernel operators and the spectral regularity lemma

Authors:
Balázs Szegedy
Affiliations:
-
Venue:
European Journal of Combinatorics
Year:
2011

Citing 4
Cited 0

Graph limits and parameter testing

Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
Limits of dense graph sequences

Journal of Combinatorial Theory Series B
Quasirandom groups

Combinatorics, Probability and Computing
Finitely forcible graphons

Journal of Combinatorial Theory Series B

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Abstract

We study the spectral aspects of the graph limit theory. We give a description of graphon convergence in terms of convergence of eigenvalues and eigenspaces. Along these lines we prove a spectral version of Szemeredi's regularity lemma. Using spectral methods we investigate group actions on graphons. As an application we show that the set of isometry invariant graphons on the sphere is closed in terms of graph convergence, however the analogous statement does not hold for the circle. This fact is rooted in the representation theory of the orthogonal group.