@inproceedings{127bcc8a179c4a5bbfbb22e0aa5317dd,
title = "A log-sobolev inequality for the multislice, with applications",
abstract = "Let κ ϵ Nℓ+ satisfy κ1+···+κℓ = n, and let Uκ denote the multislice of all strings u ∈ [ℓ]n having exactly κi coordinates equal to i, for all i ϵ [ℓ]. Consider the Markov chain on Uκ where a step is a random transposition of two coordinates of u. We show that the log-Sobolev constant ρκ for the chain satisfies (Formula presented), which is sharp up to constants whenever ℓ is constant. From this, we derive some consequences for small-set expansion and isoperimetry in the multislice, including a KKL Theorem, a Kruskal–Katona Theorem for the multislice, a Friedgut Junta Theorem, and a Nisan–Szegedy Theorem.",
keywords = "Combinatorics, Conductance, Fourier analysis, Hypercontractivity, Log-Sobolev inequality, Markov chains, Representation theory, Small-set expansion",
author = "Yuval Filmus and Ryan O{\textquoteright}Donnell and Xinyu Wu",
note = "Publisher Copyright: {\textcopyright} Yuval Filmus, Ryan O{\textquoteright}Donnell, and Xinyu Wu.; 10th Innovations in Theoretical Computer Science, ITCS 2019 ; Conference date: 10-01-2019 Through 12-01-2019",
year = "2019",
month = jan,
day = "1",
doi = "https://doi.org/10.4230/LIPIcs.ITCS.2019.34",
language = "الإنجليزيّة",
series = "Leibniz International Proceedings in Informatics, LIPIcs",
editor = "Avrim Blum",
booktitle = "10th Innovations in Theoretical Computer Science, ITCS 2019",
}