Geodesic
Unitarily Invariant Ergodic Matrices and Free Probability
Matematičeskie zametki, Tome 98 (2015) no. 6, pp. 824-831

Voir la notice de l'article provenant de la source Math-Net.Ru

Probability measures on the space of Hermitian matrices which are ergodic for the conjugation action of an infinite-dimensional unitary group are considered. It is established that the eigenvalues of random matrices distributed with respect to these measures satisfy the law of large numbers. The relationship between such models of random matrices and objects in free probability, freely infinitely divisible measures, is also established.
Keywords: unitarily invariant ergodic matrix, infinitely divisible measure, free probability, Hermitian matrix, empiric distribution of eigenvalues, free convolution, free cumulant. 
@article{MZM_2015_98_6_a2,
     author = {Al. I. Bufetov},
     title = {Unitarily {Invariant} {Ergodic} {Matrices} and {Free} {Probability}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {824--831},
     publisher = {mathdoc},
     volume = {98},
     number = {6},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2015_98_6_a2/}
}
TY  - JOUR
AU  - Al. I. Bufetov
TI  - Unitarily Invariant Ergodic Matrices and Free Probability
JO  - Matematičeskie zametki
PY  - 2015
SP  - 824
EP  - 831
VL  - 98
IS  - 6
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_2015_98_6_a2/
LA  - ru
ID  - MZM_2015_98_6_a2
ER  - 
%0 Journal Article
%A Al. I. Bufetov
%T Unitarily Invariant Ergodic Matrices and Free Probability
%J Matematičeskie zametki
%D 2015
%P 824-831
%V 98
%N 6
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_2015_98_6_a2/
%G ru
%F MZM_2015_98_6_a2
Al. I. Bufetov. Unitarily Invariant Ergodic Matrices and Free Probability. Matematičeskie zametki, Tome 98 (2015) no. 6, pp. 824-831. http://geodesic.mathdoc.fr/item/MZM_2015_98_6_a2/