Lunedi 23 gennaio
Ore 16:00, Aula di Consiglio
Seminario di Probabilità e Statistica Matematica

Domenico Marinucci, Dipartimento di Matematica, Università di Roma Tor Vergata

Titolo: A Quantitative Central Limit Theorem for the Euler-Poincaré Characteristic of Random Spherical Eigenfunctions

We establish here a Quantitative Central Limit Theorem (in Wasserstein
distance) for the Euler-Poincaré Characteristic of excursion sets of
random spherical eigenfunctions in dimension 2. Our proof is based upon a
decomposition of the Euler-Poincaré Characteristic into different
Wiener-chaos components: we prove that its asymptotic behaviour is
dominated by a single term, corresponding to the chaotic component of
order two. As a consequence, we show how the asymptotic dependence on the threshold level u is fully degenerate, i.e. the Euler-Poincaré
Characteristic converges to a single random variable times a deterministic
function of the threshold. This deterministic function has a zero at the
origin, where the variance is thus asymptotically of smaller order. Our
results can be written as an asymptotic second-order Gaussian Kinematic
Formula for the excursion sets of Gaussian spherical harmonics.
Based on a joint work with Valentina Cammarota.

Prossimo seminario: Valentina Cammarota, 31/1

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