Ciclo di Seminari - Progetto ERC grant PASCAL (Probabilistic and Statistical Techniques for Cosmological Applications) Lunedi` 9 Marzo - ore 14.00 Aula D'Antoni 1101 Dipartimento di Matematica Università di Roma Tor Vergata Speaker: Elena Villa - Università degli Studi di Milano, Dipartimento di Matematica Title: MINKOWSKI CONTENT AND MEAN DENSITY OF RANDOM CLOSED SETS: some theoretical results and statistical applications Abstract: In this talk we deal with random closed sets in R^d with integer Hausdorff dimension n<d; a problem of interest in many real applications is the study of the so-called mean density of the involved set. Namely, given a random closed set Theta with Hausdorff dimension n, it may well happen that its "induced mean measure" mu(B):=E[H^n(\Theta\cap B] (where H^n denotes the n-dimensional Hausdorff measure) is absolutely continuous with respect to the d-dimensional Lebesgue measure; in such a case, the corresponding density is named the "mean density of Theta". We will give here an overview of some recent results both on its theoretical value and on its estimation in the non-stationary setting; to this aim a stochastic version of the Minkowski content notion will play a fundamental role. Tutti gli interessati sono invitati a partecipare. ................................................................................ Valentina Cammarota, Postdoc Department of Mathematics Universita` degli Studi di Roma Tor Vergata https://sites.google.com/site/valentinacammarota/ ................................................................................ -- Open WebMail Project (http://openwebmail.org)