Some variations on a theme by P. de Jong Date: 8 September 2022, Thursday Time: 5pm AEST Statistics and Stochastic colloquium (part of the Colloquium Series of the Department of Mathematics and Statistics) at La Trobe University jointly organized with the Probability Victoria Seminar. Contact the organizers: Kostya Borovkov kostya.borovkov@gmail.com, Andriy Olenko a.olenko@latrobe.edu.au Speaker: Prof Giovanni Peccati (University of Luxembourg, Grand Duchy of Luxembourg) Abstract:In a remarkable paper from 1990, the Dutch mathematician P. de Jong proved a striking Central Limit Theorem yielding that, for a sequence of normalized and degenerate U-statistics verifying a Lindeberg-type condition, convergence to Gaussian is equivalent to the convergence of their fourth cumulants to zero. Such a result is the ancestor of the collection of “fourth-moment theorems” for non-linear functionals of random fields, that have recently played a prominent role in several question...
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