18 citations · 37 across the 25 of their papers we have counts for
6 papers · 1 filter
Freeness characterizations on free chaos spaces
Solesne Bourguin, Ivan Nourdin
This paper deals with characterizing the freeness and asymptotic freeness of free multiple integrals with respect to a free Brownian motion or a free Poisson process. We obtain thr…
Free quantitative fourth moment theorems on Wigner space
Solesne Bourguin, Simon Campese
We prove a quantitative Fourth Moment Theorem for Wigner integrals of any order with symmetric kernels, generalizing an earlier result from Kemp et al. (2012). The proof relies on…
Vector-valued semicircular limits on the free Poisson chaos
Solesne Bourguin
In this note, we prove a multidimensional counterpart of the central limit theorem on the free Poisson chaos recently proved by Bourguin and Peccati (2014). A noteworthy property o…
Poisson convergence on the free Poisson algebra
Solesne Bourguin
Based on recent findings by Bourguin and Peccati, we give a fourth moment type condition for an element of a free Poisson chaos of arbitrary order to converge to a free (centered)…
Semicircular limits on the free Poisson chaos: counterexamples to a transfer principle
Solesne Bourguin, Giovanni Peccati
We establish a class of sufficient conditions, ensuring that a sequence of multiple integrals with respect to a free Poisson measure converges to a semicircular limit. We use this…
Asymptotic Cramér type decomposition for Wiener and Wigner integrals
Solesne Bourguin, Jean-Christophe Breton
We investigate generalizations of the Cramér theorem. This theorem asserts that a Gaussian random variable can be decomposed into the sum of independent random variables if and onl…