Free Stein Kernel and Moments maps
CP Diez - arXiv preprint arXiv:2410.02470, 2024 - arxiv.org
In this paper we propose a free analogue to Fathi's construction of Stein kernels using
moment maps (2019). This is possible for a class of measures called free moment …
moment maps (2019). This is possible for a class of measures called free moment …
Free Malliavin-Stein-Dirichlet method: multidimensional semicircular approximations and chaos of a quantum Markov operator
CP Diez - arXiv preprint arXiv:2211.07595, 2022 - arxiv.org
We combine the notion of free Stein kernel and the free Malliavin calculus to provide
quantitative bounds under the free (quadratic) Wasserstein distance in the multivariate …
quantitative bounds under the free (quadratic) Wasserstein distance in the multivariate …
A note on existence of free Stein kernels
Stein kernels are a way of comparing probability distributions, defined via integration by
parts formulas. We provide two constructions of Stein kernels in free probability. One is given …
parts formulas. We provide two constructions of Stein kernels in free probability. One is given …
Free Stein kernels, free moment maps, and higher order derivatives
CP Diez - arXiv preprint arXiv:2306.00967, 2023 - arxiv.org
In this work, we describe new constructions of free Stein kernels. Firstly, in dimension one,
we propose a free analog to the construction of Stein kernels using moment maps as the …
we propose a free analog to the construction of Stein kernels using moment maps as the …
Sobolev-Wigner spaces
CP Diez - arXiv preprint arXiv:2303.13487, 2023 - arxiv.org
In this paper, we provide new results about the free Malliavin calculus on the Wigner space
first developed in the breakthrough work of Biane and Speicher. We define in this way the …
first developed in the breakthrough work of Biane and Speicher. We define in this way the …
Maximal correlation and monotonicity of free entropy and of Stein discrepancy
We introduce the maximal correlation coefficient R (M 1, M 2) between two noncommutative
probability subspaces M 1 and M 2 and show that the maximal correlation coefficient …
probability subspaces M 1 and M 2 and show that the maximal correlation coefficient …
Quelques théorèmes limites pour les matrices aléatoires, les processus non gaussiens et en probabilités libres
CP Diez - 2022 - theses.hal.science
Cette thèse se compose de trois parties distinctes et se concentre à la fois sur l'analyse
stochastique commutative et non commutative. La première partie de ce travail portera sur …
stochastique commutative et non commutative. La première partie de ce travail portera sur …