Infinite random matrices and ergodic measures

Alexei Borodin, Grigori Olshanski

Research output: Contribution to journalArticlepeer-review

59 Citations (Scopus)


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
Issue number1
Publication statusPublished - 2001
Externally publishedYes


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