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math.PR2026
Upper and Lower Bounds on Expected Soft Maxima of Gaussian Processes
Yifeng Chu, Maxim Raginsky
We obtain upper and lower bounds for "smoothed" versions of the expected supremum of centered Gaussian processes with finite or countable index sets. These so-called soft maxima ar…
math.PR2025
Talagrand Meets Talagrand: Upper and Lower Bounds on Expected Soft Maxima of Gaussian Processes with Finite Index Sets
Yifeng Chu, Maxim Raginsky
Analysis of extremal behavior of stochastic processes is a key ingredient in a wide variety of applications, including probability, statistical physics, theoretical computer scienc…
math.PR2023
A Chain Rule for the Expected Suprema of Bernoulli Processes
Yifeng Chu, Maxim Raginsky
We obtain an upper bound on the expected supremum of a Bernoulli process indexed by the image of an index set under a uniformly Lipschitz function class in terms of properties of t…