A free stochastic partial differential equation

Yoann Dabrowski

Annales de l'I.H.P. Probabilités et statistiques (2014)

  • Volume: 50, Issue: 4, page 1404-1455
  • ISSN: 0246-0203

Abstract

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We get stationary solutions of a free stochastic partial differential equation. As an application, we prove equality of non-microstate and microstate free entropy dimensions under a Lipschitz like condition on conjugate variables, assuming also the von Neumann algebra R ω embeddable. This includes an N -tuple of q -Gaussian random variables e.g. for | q | N ≤ 0 . 13 .

How to cite

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Dabrowski, Yoann. "A free stochastic partial differential equation." Annales de l'I.H.P. Probabilités et statistiques 50.4 (2014): 1404-1455. <http://eudml.org/doc/272058>.

@article{Dabrowski2014,
abstract = {We get stationary solutions of a free stochastic partial differential equation. As an application, we prove equality of non-microstate and microstate free entropy dimensions under a Lipschitz like condition on conjugate variables, assuming also the von Neumann algebra $R^\{\omega \}$ embeddable. This includes an $N$-tuple of $q$-Gaussian random variables e.g. for $|q|N\le 0.13$.},
author = {Dabrowski, Yoann},
journal = {Annales de l'I.H.P. Probabilités et statistiques},
keywords = {free stochastic partial differential equations; lower bounds on microstate free entropy dimension; free probability; $q$-gaussian variables; free stochastic partial differential equations; lower bounds on microstate free entropy dimension; free probability; -Gaussian variables},
language = {eng},
number = {4},
pages = {1404-1455},
publisher = {Gauthier-Villars},
title = {A free stochastic partial differential equation},
url = {http://eudml.org/doc/272058},
volume = {50},
year = {2014},
}

TY - JOUR
AU - Dabrowski, Yoann
TI - A free stochastic partial differential equation
JO - Annales de l'I.H.P. Probabilités et statistiques
PY - 2014
PB - Gauthier-Villars
VL - 50
IS - 4
SP - 1404
EP - 1455
AB - We get stationary solutions of a free stochastic partial differential equation. As an application, we prove equality of non-microstate and microstate free entropy dimensions under a Lipschitz like condition on conjugate variables, assuming also the von Neumann algebra $R^{\omega }$ embeddable. This includes an $N$-tuple of $q$-Gaussian random variables e.g. for $|q|N\le 0.13$.
LA - eng
KW - free stochastic partial differential equations; lower bounds on microstate free entropy dimension; free probability; $q$-gaussian variables; free stochastic partial differential equations; lower bounds on microstate free entropy dimension; free probability; -Gaussian variables
UR - http://eudml.org/doc/272058
ER -

References

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