TY - JOUR

T1 - On number rigidity for pfaffian point processes

AU - Bufetov, Alexander I.

AU - Nikitin, Pavel P.

AU - Qiu, Yanqi

PY - 2019/4/1

Y1 - 2019/4/1

N2 - 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.

AB - 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.

KW - Number rigidity

KW - Pfaffian point process

KW - Stationary point process

UR - http://www.scopus.com/inward/record.url?scp=85067826214&partnerID=8YFLogxK

U2 - 10.17323/1609-4514-2019-19-2-217-274

DO - 10.17323/1609-4514-2019-19-2-217-274

M3 - Article

AN - SCOPUS:85067826214

VL - 19

SP - 217

EP - 274

JO - Moscow Mathematical Journal

JF - Moscow Mathematical Journal

SN - 1609-3321

IS - 2

ER -