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
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
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