Guillaume Poly

Convergence in law in the second Wiener/Wigner chaos

Let L be the class of limiting laws associated with sequences in the second Wiener chaos. We exhibit a large subset

Generalization of the Nualart-Peccati criterion

L_0

Convergence Towards Linear Combinations of Chi-Squared Random Variables: A Malliavin-Based Approach

of

Multivariate Gaussian approximations on Markov chaoses

L

A bound on the 2-Wasserstein distance between linear combinations of independent random variables

satisfying that, for any

Convergence in distribution norms in the CLT for non identical distributed random variables

F_\infty

Convergence in Law Implies Convergence in Total Variation for Polynomials in Independent Gaussian, Gamma or Beta Random Variables

in

Two Properties of Vectors of Quadratic Forms in Gaussian Random Variables

L_0

Non universality for the variance of the number of real roots of random trigonometric polynomials

, the convergence of only a finite number of cumulants suffices to imply the convergence in law of any sequence in the second Wiener chaos to

A weak Cramér condition and application to Edgeworth expansions

F_\infty