Infinite random matrices and ergodic measures

Alexei Borodin, Grigori Olshanski

Research output: Contribution to journalArticlepeer-review

59 Citations (Scopus)

Abstract

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.

Original languageEnglish
Pages (from-to)87-123
Number of pages37
JournalCommunications in Mathematical Physics
Volume223
Issue number1
DOIs
Publication statusPublished - 2001
Externally publishedYes

Fingerprint

Dive into the research topics of 'Infinite random matrices and ergodic measures'. Together they form a unique fingerprint.

Cite this