Electronic Journal of Probability

Pfaffian Formulae for One Dimensional Coalescing and Annihilating Systems

Roger Tribe and Oleg Zaboronski

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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

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

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

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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]

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

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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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