Szemerédi's Regularity Lemma via Martingales

Pandelis Dodos, Vassilis Kanellopoulos, Thodoris Karageorgos

Abstract


We prove a variant of the abstract probabilistic version of Szemerédi's regularity lemma, due to Tao, which applies to a number of structures (including graphs, hypergraphs, hypercubes, graphons, and many more) and works for random variables in $L_p$ for any $p>1$. Our approach is based on martingale difference sequences.

Keywords


Szemerédi's regularity lemma, Semiring, Norm, Martingale difference sequences

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