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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…
math.PR2024
Entropy and curvature: beyond the Peres-Tetali conjecture
Pietro Caputo, Florentin Münch, Justin Salez
We study Markov chains with non-negative sectional curvature on finite metric spaces. Neither reversibility, nor the restriction to a particular combinatorial distance are imposed.…