5 papers
Nonlinear Exchange Dynamics for Independent Sets
Mehrad Abbaszadeh Minab, Pietro Caputo, Zongchen Chen +2
In recent years, nonlinear dynamics derived from kinetic theory have gained attention in the context of sampling configurations of spin systems such as the Ising model. We focus on…
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…
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…
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…
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.…