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math.PR2025
Factorizations of relative entropy using stochastic localization
Pietro Caputo, Zongchen Chen, Daniel Parisi
We derive entropy factorization estimates for spin systems using the stochastic localization approach proposed by Eldan and Chen-Eldan, which, in this context, is equivalent to the…
math.PR2024
Entropy Contractions in Markov Chains: Half-Step, Full-Step and Continuous-Time
Pietro Caputo, Zongchen Chen, Yuzhou Gu +1
This paper considers the speed of convergence (mixing) of a finite Markov kernel with respect to the Kullback-Leibler divergence (entropy). Given a Markov kernel one defines ei…
math.PR2024
Entropy factorization via curvature
Pietro Caputo, Justin Salez
We develop a new framework for establishing approximate factorization of entropy on arbitrary probability spaces, using a geometric notion known as non-negative sectional curvature…