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• W4214883825 abstract "Let κ∈N+ℓ 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∈[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 ϱκ−1≤n⋅∑i=1ℓ12log2(4n∕κi), 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." @default.
• W4214883825 created "2022-03-05" @default.
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• W4214883825 date "2022-01-01" @default.
• W4214883825 modified "2023-09-30" @default.
• W4214883825 title "Log-Sobolev inequality for the multislice, with applications" @default.
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• W4214883825 doi "https://doi.org/10.1214/22-ejp749" @default.
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