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math.PR2024
Large Deviation Analysis for Canonical Gibbs Measures
Christian Hirsch, Martina Petráková
In this paper, we present a large-deviation theory developed for functionals of canonical Gibbs processes, i.e., Gibbs processes with respect to the binomial point process. We stud…
math.PR2024
Functional central limit theorem for topological functionals of Gaussian critical points
Christian Hirsch, Raphaël Lachièze-Rey
We consider Betti numbers of the excursion of a smooth Euclidean Gaussian field restricted to a rectangular window, in the asymptotics where the window grows to R^d . With motivati…
math.PR2024★ 4 cited
Large deviations of one-hidden-layer neural networks
Christian Hirsch, Daniel Willhalm
We study large deviations in the context of stochastic gradient descent for one-hidden-layer neural networks with quadratic loss. We derive a quenched large deviation principle, wh…