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Asymptotic expansions for a class of Fredholm Pfaffians and interacting particle systems
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FitzGerald, William Robert, Tribe, Roger and Zaboronski, Oleg V. (2022) Asymptotic expansions for a class of Fredholm Pfaffians and interacting particle systems. Annals of Probability, 50 (6). pp. 2409-2474. doi:10.1214/22-AOP1586 ISSN 0091-1798.
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WRAP-Asymptotic-expansions-class-Fredholm-Pfaffians-particle-systems-2022.pdf - Accepted Version - Requires a PDF viewer. Download (946Kb) | Preview |
Official URL: https://doi.org/10.1214/22-AOP1586
Abstract
Motivated by the phenomenon of duality for interacting particle systems, we introduce two classes of Pfaffian kernels describing a number of Pfaffian point processes in the “bulk” and at the “edge.” Using the probabilistic method due to Mark Kac, we prove two Szegő-type asymptotic expansion theorems for the corresponding Fredholm Pfaffians. The idea of the proof is to introduce an effective random walk with transition density determined by the Pfaffian kernel, express the logarithm of the Fredholm Pfaffian through expectations with respect to the random walk, and analyse the expectations using general results on random walks. We demonstrate the utility of the theorems by calculating asymptotics for the empty interval and noncrossing probabilities for a number of examples of Pfaffian point processes: coalescing/annihilating Brownian motions, massive coalescing Brownian motions, real zeros of Gaussian power series and Kac polynomials, and real eigenvalues for the real Ginibre ensemble.
| Item Type: | Journal Article | ||||||||
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| Subjects: | Q Science > QA Mathematics | ||||||||
| Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||||||
| Library of Congress Subject Headings (LCSH): | Random matrices, Brownian motion processes, Operator theory, Vertex operator algebras, Point processes -- Mathematical models | ||||||||
| Journal or Publication Title: | Annals of Probability | ||||||||
| Publisher: | Institute of Mathematical Statistics | ||||||||
| ISSN: | 0091-1798 | ||||||||
| Official Date: | November 2022 | ||||||||
| Dates: |
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| Volume: | 50 | ||||||||
| Number: | 6 | ||||||||
| Page Range: | pp. 2409-2474 | ||||||||
| DOI: | 10.1214/22-AOP1586 | ||||||||
| Status: | Peer Reviewed | ||||||||
| Publication Status: | Published | ||||||||
| Access rights to Published version: | Open Access (Creative Commons) | ||||||||
| Copyright Holders: | Copyright © 2022 Institute of Mathematical Statistics | ||||||||
| Date of first compliant deposit: | 24 May 2022 | ||||||||
| Date of first compliant Open Access: | 25 May 2022 | ||||||||
| RIOXX Funder/Project Grant: |
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