Ciclo di Seminari - Progetto ERC grant PASCAL (Probabilistic and Statistical Techniques for Cosmological Applications) Annuncio di Colloquium al Dipartimento di Matematica, Universita` di Roma Tor Vergata Mercoledi` 18 novembre 2015 in Aula Dal Passo Ore 15 Giovanni PECCATI (Universite' du Luxenbourg) Connecting and projecting random points: a gate to novel functional estimates Abstract: I will formulate two simple models of stochastic geometry: the first one involves the projection of a random Gaussian point on a closed convex cone, and the second one consists in the construction of a random graph on the plane. For each of them, I will explain how the fluctuations of several key quantities can be controlled by using functional inequalities, like Poincare', logarithmic Sobolev and information/transport estimates. The resulting bounds will allow us to present a number of quantitative results that are part of a growing body of literature focussing on probabilistic approximations via variational techniques, that have been successfully applied to fields as diverse as compressed sensing, the geometry of random fields on homogeneous spaces, polymer models, computer sciences and time series analysis. The presentation will be adapted to a general mathematical audience, and is based on a large number of contributions by many authors, spread over almost a decade. Ore 16: coffee break Ore 16:45 Seminario Alessandro Arlotto (Duke University) Finite Horizon Markov Decision Problems and a Central Limit Theorem for Total Reward Abstract: We prove a central limit theorem for a class of additive processes that arise naturally in the theory of finite horizon Markov decision problems. The main theorem generalizes a classic result of Dobrushin (1956) for temporally non-homogeneous Markov chains, and the principal innovation is that here the summands are permitted to depend on both the current state and a bounded number of future states of the chain. We show through several examples that this added flexibility gives one a direct path to asymptotic normality of the optimal total reward of finite horizon Markov decision problems. The same examples also explain why such results are not easily obtained by alternative Markovian techniques such as enlargement of the state space. Tutti gli interessati sono invitati a partecipare. ………………………………………………………………….. Valentina Cammarota Department of Mathematics Universita` degli Studi di Roma Tor Vergata http://www.mat.uniroma2.it/english.php https://sites.google.com/site/valentinacammarota/