Ho il piacere di invitarvi al seguente seminario, che si terrà Giovedì 27 Ottobre, alle 12:00, in aula 2BC30 della Torre Archimede presso il Dipartimento di Matematica dell'Università degli Studi di Padova.

SPEAKER: Giovanni Conforti

AFFILIATION: University of Leipzig

TITLE: Some quantitative results about bridges and Entropic interpolations of probability measures

ABSTRACT: In the first part of the talk I will discuss quantitative results about the bridges of the Langevin dynamics and the associated reciprocal processes.They include an equivalence between gradient estimates for bridge semigroups and couplings, comparison principles, and a Logarithmic Sobolev inequality. All results are based on a seemingly new expression of the drift of a bridge in terms of the reciprocal characteristic, which, roughly speaking, is the ``acceleration" of a bridge. The analogy between reciprocal characteristic and acceleration also allows to view our results as a probabilistic version of well known facts about ODEs. Bridges can be used to construct interpolations of probability measures. The resulting curve, called entropic interpolation, is a stochastic counterpart to the displacement interpolation. If time allows, I will discuss connections with gradient flows on Wasserstein space and an estimate of the marginal entropy along entropic interpolations which in the small noise limit gives back the well known convexity of the entropy along displacement interpolations.

The talk is partially based on joint work with Max von Renesse.

Paolo Dai Pra Dipartimento di Matematica Via Trieste, 63 35121 Padova Tel. +39 0498271361 Fax +39 0498271428 daipra@math.unipd.it