RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PERSONAL OFFICE
 General information Latest issue Forthcoming papers Archive Impact factor Subscription Guidelines for authors License agreement Submit a manuscript Search papers Search references RSS Latest issue Current issues Archive issues What is RSS

 Izv. RAN. Ser. Mat.: Year: Volume: Issue: Page: Find

 Izv. RAN. Ser. Mat., 2015, Volume 79, Issue 6, Pages 18–64 (Mi izv8383)

Infinite determinantal measures and the ergodic decomposition of infinite Pickrell measures. I. Construction of infinite determinantal measures

A. I. Bufetovabcd

a Steklov Mathematical Institute of Russian Academy of Sciences, Moscow
b Institute for Information Transmission Problems of the Russian Academy of Sciences (Kharkevich Institute), Moscow
c National Research University "Higher School of Economics" (HSE), Moscow
d Aix-Marseille Université

Abstract: This paper is the first in a series of three. We give an explicit description of the ergodic decomposition of infinite Pickrell measures on the space of infinite complex matrices. A key role is played by the construction of $\sigma$-finite analogues of determinantal measures on spaces of configurations, including the infinite Bessel process, a scaling limit of the $\sigma$-finite analogues of the Jacobi orthogonal polynomial ensembles. Our main result identifies the infinite Bessel process with the decomposing measure of an infinite Pickrell measure.

Keywords: determinantal processes, infinite determinantal measures, ergodic decomposition, infinite harmonic analysis, infinite unitary group, scaling limits, Jacobi polynomials, Harish-Chandra–Itzykson–Zuber orbit integral.

 Funding Agency Grant Number Agence Nationale de la Recherche ANR-11-IDEX-0001-02 Ministry of Education and Science of the Russian Federation ÌÄ-2859.2014.1 Russian Academy of Sciences - Federal Agency for Scientific Organizations 0014-2015-0006 Russian Foundation for Basic Research 13-01-12449 îôè_ì This work was supported by the project A*MIDEX (no. ANR-11-IDEX-0001-02) of the French Republic Government Programme ‘Investing in the Future’ carried out by the French National Agency of Scientific Research (ANR). It was also supported by the Programme of Governmental Support of Scientific Research of Young Russian Scholars, Candidates and Doctors of Sciences (grant no. MD-2859.2014.1), the Programme of Fundamental Research of RAS no. I.28P ‘Mathematical problems of modern control theory’ (project no. 0014-2015-0006 ‘Ergodic theory and dynamical systems’), the subsidy for governmental support of leading universities of the Russian Federation aimed at raising their competitiveness among world leading scientific and educational centres, distributed to the National Research University ‘Higher School of Economics’, and the RFBR (grant no. 13-01-12449-ofi_m).

DOI: https://doi.org/10.4213/im8383

Full text: PDF file (897 kB)
References: PDF file   HTML file

English version:
Izvestiya: Mathematics, 2015, 79:6, 1111–1156

Bibliographic databases:

Document Type: Article
UDC: 517.938+519.21
MSC: 20C32, 22D40, 28C10, 28D15, 43A05, 60B15, 60G55

Citation: A. I. Bufetov, “Infinite determinantal measures and the ergodic decomposition of infinite Pickrell measures. I. Construction of infinite determinantal measures”, Izv. RAN. Ser. Mat., 79:6 (2015), 18–64; Izv. Math., 79:6 (2015), 1111–1156

Citation in format AMSBIB
\Bibitem{Buf15} \by A.~I.~Bufetov \paper Infinite determinantal measures and the ergodic decomposition of infinite Pickrell measures. I. Construction of infinite determinantal measures \jour Izv. RAN. Ser. Mat. \yr 2015 \vol 79 \issue 6 \pages 18--64 \mathnet{http://mi.mathnet.ru/izv8383} \crossref{https://doi.org/10.4213/im8383} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=3438464} \adsnasa{http://adsabs.harvard.edu/cgi-bin/bib_query?2015IzMat..79.1111B} \elib{http://elibrary.ru/item.asp?id=24850001} \transl \jour Izv. Math. \yr 2015 \vol 79 \issue 6 \pages 1111--1156 \crossref{https://doi.org/10.1070/IM2015v079n06ABEH002775} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000371441400002} \scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84960498330} 

• http://mi.mathnet.ru/eng/izv8383
• https://doi.org/10.4213/im8383
• http://mi.mathnet.ru/eng/izv/v79/i6/p18

 SHARE:

Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles
Cycle of papers

This publication is cited in the following articles:
1. A. I. Bufetov, “Infinite determinantal measures and the ergodic decomposition of infinite Pickrell measures. II. Convergence of infinite determinantal measures”, Izv. Math., 80:2 (2016), 299–315
2. A. I. Bufetov, “Infinite determinantal measures and the ergodic decomposition of infinite Pickrell measures. III. The infinite Bessel process as the limit of the radial parts of finite-dimensional projections of infinite Pickrell measures”, Izv. Math., 80:6 (2016), 1035–1056
3. A. I. Bufetov, Y. Qiu, “The explicit formulae for scaling limits in the ergodic decomposition of infinite Pickrell measures”, Ark. Mat., 54:2 (2016), 403–435
4. Alexander I. Bufetov, “A Palm hierarchy for determinantal point processes with the Bessel kernel”, Proc. Steklov Inst. Math., 297 (2017), 90–97
5. Y. Qiu, “Infinite random matrices & ergodic decomposition of finite and infinite Hua-Pickrell measures”, Adv. Math., 308 (2017), 1209–1268
•  Number of views: This page: 379 Full text: 25 References: 35 First page: 34