Regularity method and large deviation principles for the Erdős–Rényi hypergraph

Nicholas Cook (Duke)

11-Jun-2021, 13:00-14:00 (3 years ago)

Abstract: In recent years there has been intense activity on the problem of estimating the upper tail for counts of a fixed subgraph in a sparse Erdős–Rényi graph, combining tools and perspectives from diverse areas such as extremal graph theory, statistical physics, stochastic analysis and spectral theory. I will discuss some recent extensions of these results to the hypergraph setting. Our approach rests on new decomposition theorems and counting lemmas for sparse Bernoulli tensors, extending classic results from the regularity method for dense graphs. These results are formulated in terms of a new class of cut-type norms specially tailored for the sparse setting. Based on joint work with Amir Dembo and Huy Tuan Pham.

combinatorics

Audience: researchers in the topic


Warwick Combinatorics Seminar

Series comments: This is the online combinatorics seminar at Warwick.

Organizers: Jan Grebik, Oleg Pikhurko
Curator: Hong Liu*
*contact for this listing

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