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Thesis

Sidorenko's conjecture, graph norms, and pseudorandomness

Abstract:

This thesis is primarily concerned with correlation inequalities between the number of homomorphic copies of different graphs. In particular, many of the results relate to a beautiful conjecture of Sidorenko, which roughly states that the number of copies of a bipartite graph H in a graph G is asymptotically minimised when G is the Erdos Reyni random graph.

The first part of the thesis discusses recent approaches to attack Sidorenko's conjecture. We firstly prove that every gr...

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Role:
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Type of award:
DPhil
Level of award:
Doctoral
Awarding institution:
University of Oxford
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