21 citations · 26 across the 7 of their papers we have counts for
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Universality and Fourth Moment Theorem for homogeneous sums. Orthogonal polynomials and apolarity
Rosaria Simone
The aim of the dissertation is threefold: the first two parts are devoted to explore the Fourth Moment Theorem and universality properties for homogeneous sums, while the last part…
Multidimensional limit theorems for homogeneous sums: a general transfer principle
Ivan Nourdin, Giovanni Peccati, Guillaume Poly +1
The aim of the present paper is to establish the multidimensional counterpart of the \textit{fourth moment criterion} for homogeneous sums in independent leptokurtic and mesokurtic…
Classical and free Fourth Moment Theorems: universality and thresholds
Ivan Nourdin, Giovanni Peccati, Guillaume Poly +1
Let be a centered random variable with unit variance, zero third moment, and such that . Let denote a normalized sequence of homogeneous sums…
Universality of free homogeneous sums in every dimension
R. Simone
We prove a general multidimensional invariance principle for a family of U-statistics based on freely independent non-commutative random variables of the type , where $U_n(…