Ciclo di Seminari - Progetto ERC grant PASCAL (Probabilistic and Statistical Techniques for Cosmological Applications)
Mercoledi` 25 marzo ore 14 - 16
Aula D'Antoni 1101 Dipartimento di Matematica Università di Roma Tor Vergata
Speakers: Armin Schwartzman & Dang Cheng Department of Statistics, North Carolina State University
Title: Distribution of the Height of Local Maxima of Gaussian Random Fields
Abstract: Let {f(t): t \in T} be a smooth Gaussian random field over a parameter space T, where T may be a subset of Euclidean space or, more generally, a Riemannian manifold. We provide a general formula for the distribution of the height of a local maximum P { f(t_0)>u | t_0 is a local maximum of f(t) } when f is non-stationary. Moreover, we establish asymptotic approximations for the overshoot distribution of a local maximum P { f(t_0)>u+v | t_0 is a local maximum of f(t) and f(t_0)>v } as v \to \infty. Assuming further that f is isotropic, we apply techniques from random matrices theory related to the Gaussian orthogonal ensemble to compute such conditional probabilities explicitly when T is Euclidean or a sphere of arbitrary dimension. Such calculations are motivated by the statistical problem of detecting peaks in the presence of smooth Gaussian noise.
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................................................................................ Valentina Cammarota, Postdoc Department of Mathematics Universita` degli Studi di Roma Tor Vergata https://sites.google.com/site/valentinacammarota/ ................................................................................
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