Infinite random matrices and ergodic measures
Borodin, Alexei ; Olshanski, Grigori
arXiv, 0010015 / Harvested from arXiv
Text on arXiv
We introduce and study a 2-parameter family of unitarily invariant probability measures on the space of infinite Hermitian matrices. We show that the decomposition of a measure from this family on ergodic components is described by a determinantal point process on the real line. The correlation kernel for this process is explicitly computed. At certain values of parameters the kernel turns into the well-known sine kernel which describes the local correlation in Circular and Gaussian Unitary Ensembles. Thus, the random point configuration of the sine process is interpreted as the random set of ``eigenvalues'' of infinite Hermitian matrices distributed according to the corresponding measure.
Publié le : 2000-10-11
Classification:  Mathematical Physics,  Mathematics - Probability,  Mathematics - Representation Theory 
@article{0010015,
     author = {Borodin, Alexei and Olshanski, Grigori},
     title = {Infinite random matrices and ergodic measures},
     journal = {arXiv},
     volume = {2000},
     number = {0},
     year = {2000},
     language = {en},
     url = {http://dml.mathdoc.fr/item/0010015}
}

Borodin, Alexei; Olshanski, Grigori. Infinite random matrices and ergodic measures. arXiv, Tome 2000 (2000) no. 0, . http://gdmltest.u-ga.fr/item/0010015/