Infinite determinantal measures | Zendy

Alexander I. Bufetov | Zendy

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Infinite determinantal measures

Author(s) -

Alexander I. Bufetov

Publication year - 2013

Publication title -

electronic research announcements

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.865

H-Index - 23

ISSN - 1935-9179

DOI - 10.3934/era.2013.20.12

Subject(s) - determinantal point process , ergodic theory , mathematics , multiplicative function , measure (data warehouse) , integrable system , pure mathematics , infinite product , rank (graph theory) , point process , product (mathematics) , probability measure , discrete mathematics , combinatorics , mathematical analysis , random matrix , computer science , physics , statistics , quantum mechanics , database , eigenvalues and eigenvectors , geometry

International audienceInfinite determinantal measures introduced in this note are inductive limits of determinantal measures on an exhausting family of subsets of the phase space. Alternatively, an infinite determinantal measure can be described as a product of a determinantal point process and a convergent, but not integrable, multiplicative functional. Theorem 2, the main result announced in this note, gives an explicit description for the ergodic decomposition of infinite Pickrell measures on the spaces of infinite complex matrices in terms of infinite determi-nantal measures obtained by finite-rank perturbations of Bessel point processes

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