Bounds on the deficit in the logarithmic Sobolev inequality
Sergey Bobkov (UMN-MATH), Nathael Gozlan (LAMA), Cyril Roberto, (MODAL'X), Paul-Marie Samson (LAMA)
TL;DR
This paper investigates the deficit in the Gaussian logarithmic Sobolev inequality, providing bounds using transport and information-theoretic distances to better understand the inequality's stability.
Contribution
It introduces new bounds on the deficit in the Gaussian logarithmic Sobolev inequality utilizing transport and information distances.
Findings
Derived bounds on the deficit using transport distances
Estimated the deficit with information-theoretic measures
Enhanced understanding of the inequality's stability
Abstract
The de cit in the logarithmic Sobolev inequality for the Gaussian measure is considered and estimated by means of transport and information-theoretic distances.
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Taxonomy
TopicsDiverse Research Studies Overview · Advanced Harmonic Analysis Research · Nonlinear Partial Differential Equations