Moscow Mathematical Journal

Volume 19, Issue 2, April–June 2019 pp. 217–274.

On Number Rigidity for Pfaffian Point Processes

Authors: Alexander I. Bufetov (1), Pavel P. Nikitin (2), and Yanqi Qiu (3)
Author institution:(1) Aix-Marseille Université, Centrale Marseille, CNRS, Institut de Mathématiques de Marseille, UMR7373, 39 Rue F. Joliot Curie 13453, Marseille, France;
Steklov Mathematical Institute of RAS, Moscow, Russia
(2) St. Petersburg Department of V.A.Steklov Institute of Mathematics of the Russian Academy of Sciences, 27 Fontanka, 191023, St. Petersburg, Russia;
St. Petersburg State University, St. Petersburg, Russia
(3) Institute of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China

Summary:

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.

2010 Math. Subj. Class. Primary: 60G55; Secondary: 60G10.

Keywords: Pfaffian point process, stationary point process, number rigidity.

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