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On number rigidity for Pfaffian point processes
Alexander I. Bufetovab, Pavel P. Nikitincd, Yanqi Qiue a Aix-Marseille Université, Centrale Marseille, CNRS, Institut de Mathématiques de Marseille, UMR7373, 39 Rue F. Joliot Curie 13453, Marseille, France
b Steklov Mathematical Institute of RAS, Moscow, Russia
c St. Petersburg Department of V.A. Steklov Institute of Mathematics of the Russian Academy of Sciences, 27 Fontanka, 191023, St. Petersburg, Russia
d St. Petersburg State University, St. Petersburg, Russia
e Institute of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China
Abstract:
Our first result states that the orthogonal and symplectic Bessel
processes are rigid in the sense of Ghosh and Peres. Our argument in
the Bessel case proceeds by an estimate of the variance of additive
statistics in the spirit of Ghosh and Peres. Second, a sufficient
condition for number rigidity of stationary Pfaffian processes,
relying on the Kolmogorov criterion for interpolation of stationary
processes and applicable, in particular, to Pfaffian sine processes,
is given in terms of the asymptotics of the spectral measure for
additive statistics.
Key words and phrases:
Pfaffian point process, stationary point process, number rigidity.
DOI:
https://doi.org/10.17323/1609-4514-2019-19-2-217-274
Full text:
http://www.mathjournals.org/.../2019-019-002-003.html
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Bibliographic databases:
MSC: Primary 60G55; Secondary 60G10
Citation:
Alexander I. Bufetov, Pavel P. Nikitin, Yanqi Qiu, “On number rigidity for Pfaffian point processes”, Mosc. Math. J., 19:2 (2019), 217–274
Citation in format AMSBIB
\Bibitem{BufNikQiu19}
\by Alexander~I.~Bufetov, Pavel~P.~Nikitin, Yanqi~Qiu
\paper On number rigidity for Pfaffian point processes
\jour Mosc. Math.~J.
\yr 2019
\vol 19
\issue 2
\pages 217--274
\mathnet{http://mi.mathnet.ru/mmj734}
\crossref{https://doi.org/10.17323/1609-4514-2019-19-2-217-274}
Linking options:
http://mi.mathnet.ru/eng/mmj734 http://mi.mathnet.ru/eng/mmj/v19/i2/p217
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