Pfaffian Formulae for One Dimensional Coalescing and Annihilating Systems

Roger Tribe (University of Warwick)
Oleg Zaboronski (University of Warwick)

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.

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Pages: 2080-2103

Publication Date: November 4, 2011

DOI: 10.1214/EJP.v16-942

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