Translator Disclaimer
May 2021 Conditional measures for Pfaffian point processes: Conditioning on a bounded domain
Alexander I. Bufetov, Fabio Deelan Cunden, Yanqi Qiu
Author Affiliations +
Ann. Inst. H. Poincaré Probab. Statist. 57(2): 856-871 (May 2021). DOI: 10.1214/20-AIHP1099

Abstract

For a Pfaffian point process we show that its Palm measures, its normalised compositions with multiplicative functionals, and its conditional measures with respect to fixing the configuration in a bounded subset are Pfaffian point processes whose kernels we find explicitly.

Pour un processus Pfaffien, nous démontrons que ses mesures de Palm, ses compositions avec les fonctionnelles multiplicatives normalisdées, ainsi que ses mesures conditionnelles obtenues en fixant la configuration dans un sous-ensemble borndé, sont encore des processus Pfaffiens dont les noyaux de corrdélation sont explicitement trouvdés.

Acknowledgements

We are deeply grateful to Sergei Korotkih for useful discussions. AB’s research is supported by the European Research Council (ERC) under the European Union Horizon 2020 research and innovation programme, grant 647133 (ICHAOS), by the Agence Nationale de Recherche, project ANR-18-CE40-0035, and by the Russian Foundation for Basic Research, grant 18-31-20031. The research of FDC is supported by the European Research Council (Grant Number 669306) and partially supported by Gruppo Nazionale di Fisica Matematica GNFM-INdAM. The research of YQ is supported by grants NSFC Y7116335K1, NSFC 11801547 and NSFC 11688101 of National Natural Science Foundation of China. FDC would also like to thank the organisers of the research school ‘Gaz de Coulomb, intégrabilité et équations de Painlevé 2019’ at CIRM – Marseille, where this work was started.

Citation

Download Citation

Alexander I. Bufetov. Fabio Deelan Cunden. Yanqi Qiu. "Conditional measures for Pfaffian point processes: Conditioning on a bounded domain." Ann. Inst. H. Poincaré Probab. Statist. 57 (2) 856 - 871, May 2021. https://doi.org/10.1214/20-AIHP1099

Information

Received: 24 December 2019; Revised: 14 August 2020; Accepted: 27 August 2020; Published: May 2021
First available in Project Euclid: 13 May 2021

Digital Object Identifier: 10.1214/20-AIHP1099

Subjects:
Primary: 60G55
Secondary: 15B33

Rights: Copyright © 2021 Association des Publications de l’Institut Henri Poincaré

JOURNAL ARTICLE
16 PAGES

This article is only available to subscribers.
It is not available for individual sale.
+ SAVE TO MY LIBRARY

SHARE
Vol.57 • No. 2 • May 2021
Back to Top