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Creators/Authors contains: "Pinto, Renato Ferreira"

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  1. ; (, International Conference on Randomization and Computation (RANDOM)
    We study the spectral gap of subgraphs of the hypercube induced by monotone subsets of vertices. For a monotone subset A ⊆ {0, 1}n of density μ(A), the previous best lower bound on the spectral gap, due to Cohen [Coh16], was γ ≳ μ(A)/n2, improving upon the earlier bound γ ≳ μ(A)2/n2 established by Ding and Mossel [DM14]. In this paper, we prove the optimal lower bound γ ≳ μ(A)/n. As a corollary, we improve the mixing time upper bound of the random walk on constant-density monotone sets from O(n3), as shown by Ding and Mossel, to O(n2). Along the way, we develop two new inequalities that may be of independent interest: (1) a directed L2-Poincar´e inequality on the hypercube, and (2) an “approximate” FKG inequality for monotone sets 
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    Free, publicly-accessible full text available August 11, 2026