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Near log-convexity of heat and the k-Hamming distance problem

Mert Saglam, UW CS
Monday, April 8, 2019 - 2:30pm to 3:30pm
MEB 238

We answer a 1982 conjecture of Erdős and Simonovits about the growth of number of k-walks in a graph, which incidentally was studied even earlier by Blakley and and Dixon in 1966. We prove this conjecture in a more general setup than the earlier treatment, furthermore, through a refinement and strengthening of this inequality, we resolve two related open questions in complexity theory: the communication complexity of the k-Hamming distance is Ω(k log k) and that consequently any property tester for k-linearity requires Ω(k log k) queries.

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