Using Itô’s calculus, we study the large deviations
properties of the law of the spectral measure of the Hermitian Brownian
motion.We extend this strategy to the symmetric, unitary and Wishart processes.
This dynamical approach is generalized to the study of the large deviations of
the non-commutative laws of several independent Hermitian Brownian motions. As
a consequence, we can bound from above entropies defined in the spirit of the
microstates entropy introduced by Voiculescu.
Publié le : 2001-07-14
Classification:
Large deviations,
random matrices,
non-commutative measure,
integration,
60F10,
15A52,
46L50
@article{1015345602,
author = {Cabanal Duvillard, T. and Guionnet, A.},
title = {Large Deviations Upper Bounds for the Laws of Matrix-Valued
Processes and Non-Communicative Entropies},
journal = {Ann. Probab.},
volume = {29},
number = {1},
year = {2001},
pages = { 1205-1261},
language = {en},
url = {http://dml.mathdoc.fr/item/1015345602}
}
Cabanal Duvillard, T.; Guionnet, A. Large Deviations Upper Bounds for the Laws of Matrix-Valued
Processes and Non-Communicative Entropies. Ann. Probab., Tome 29 (2001) no. 1, pp. 1205-1261. http://gdmltest.u-ga.fr/item/1015345602/