Electronic Journal of Probability

Pfaffian Formulae for One Dimensional Coalescing and Annihilating Systems

Roger Tribe and Oleg Zaboronski

Full-text: Open access

Abstract

The paper considers instantly coalescing, or instantly annihilating, systems of one-dimensional Brownian particles on the real line. Under maximal entrance laws, the distribution of the particles at a fixed time is shown to be Pfaffian point processes closely related to the Pfaffian point process describing one dimensional distribution of real eigenvalues in the real Ginibre ensemble of random matrices. As an application, an exact large time asymptotic for the $n$-point density function for coalescing particles is derived.

Article information

Source
Electron. J. Probab., Volume 16 (2011), paper no. 76, 2080-2103.

Dates
Accepted: 4 November 2011
First available in Project Euclid: 1 June 2016

Permanent link to this document
https://projecteuclid.org/euclid.ejp/1464820245

Digital Object Identifier
doi:10.1214/EJP.v16-942

Mathematical Reviews number (MathSciNet)
MR2851057

Zentralblatt MATH identifier
1244.60097

Subjects
Primary: 60B20: Random matrices (probabilistic aspects; for algebraic aspects see 15B52)
Secondary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43] 82C22: Interacting particle systems [See also 60K35]

Keywords
annihilating/coalescing Brownian motions real Ginibre ensemble random matrices Pfaffian point processes

Rights
This work is licensed under aCreative Commons Attribution 3.0 License.

Citation

Tribe, Roger; Zaboronski, Oleg. Pfaffian Formulae for One Dimensional Coalescing and Annihilating Systems. Electron. J. Probab. 16 (2011), paper no. 76, 2080--2103. doi:10.1214/EJP.v16-942. https://projecteuclid.org/euclid.ejp/1464820245


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