On Number Rigidity for Pfaffian Point Processes

IF 0.6 4区数学 Q3 MATHEMATICS

Moscow Mathematical Journal Pub Date : 2018-10-22 DOI:10.17323/1609-4514-2019-19-2-217-274

A. Bufetov, P. Nikitin, Yanqi Qiu

引用次数: 9

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.

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关于pfaffan点过程的数刚性

我们的第一个结果表明正交和辛贝塞尔过程在Ghosh和Peres意义上是刚性的。我们在贝塞尔案例中的论证是根据Ghosh和Peres的精神对加性统计的方差进行估计的。其次，根据可加统计量谱测度的渐近性，给出了平稳Pfaffian过程数刚性的充分条件，该条件依赖于平稳过程的Kolmogorov插值准则，尤其适用于Pfaffian正弦过程。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Moscow Mathematical Journal 数学-数学

CiteScore

1.40

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： The Moscow Mathematical Journal (MMJ) is an international quarterly published (paper and electronic) by the Independent University of Moscow and the department of mathematics of the Higher School of Economics, and distributed by the American Mathematical Society. MMJ presents highest quality research and research-expository papers in mathematics from all over the world. Its purpose is to bring together different branches of our science and to achieve the broadest possible outlook on mathematics, characteristic of the Moscow mathematical school in general and of the Independent University of Moscow in particular. An important specific trait of the journal is that it especially encourages research-expository papers, which must contain new important results and include detailed introductions, placing the achievements in the context of other studies and explaining the motivation behind the research. The aim is to make the articles — at least the formulation of the main results and their significance — understandable to a wide mathematical audience rather than to a narrow class of specialists.