Titlebook: High Dimensional Probability IX; The Ethereal Volume Rados?aw Adamczak,Nathael Gozlan,Mokshay Madiman Conference proceedings 2023 The Edito

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Boolean Functions with Small Second-Order Influences on the Discrete Cubeuss space has been investigated in detail, the present note studies it in a more specific context of Boolean functions on the discrete cube. Some bounds that Tanguy obtained in Tanguy (J Theoret Probab 33:692–714, 2020) as applications of his more general approach are extended and complemented.

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Sudakov Minoration for Products of Radial-Type Log-Concave Measuresnumber of points from the index set are well separated, then we can provide an optimal type lower bound for the mean value of the supremum of the process. Together with the generic chaining argument, the property can be used to fully characterize the mean value of the supremum of the stochastic proc

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