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 …

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 …

Free Stein irregularity and dimension

I Charlesworth, B Nelson - arXiv preprint arXiv:1902.02379, 2019 - arxiv.org
We introduce a free probabilistic quantity called free Stein irregularity, which is defined in
terms of free Stein discrepancies. It turns out that this quantity is related via a simple formula …

Free Zero Bias and Infinite Divisibility

L Goldstein, T Kemp - arXiv preprint arXiv:2403.19860, 2024 - arxiv.org
The (classical) zero bias is a transformation of centered, finite variance probability
distributions, often expressed in terms of random variables $ X\mapsto X^\ast …

Stability of the Poincar\'e-Korn inequality

TA Courtade, M Fathi - arXiv preprint arXiv:2405.01441, 2024 - arxiv.org
arXiv:2405.01441v1 [math.AP] 2 May 2024 Page 1 arXiv:2405.01441v1 [math.AP] 2 May 2024
Stability of the Poincaré–Korn inequality Thomas A. Courtade∗ Max Fathi† May 2nd 2024 …

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 …

Maximal correlation and monotonicity of free entropy and of Stein discrepancy

B Dadoun, P Youssef - 2021 - projecteuclid.org
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 …

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 …