@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",

}