Pfaffian formulae for one dimensional coalescing and annihilating systems

Details Pfaffian formulae for one dimensional coalescing and annihilating systems Pfaffian formulae for one dimensional coalescing and annihilating systems

2010-09-23

arxiv.org/abs/1009.4565v4

Electronic Journal of Probability, vol. 16, Article 76 (2011)

Mathematics

Probability

26 pages, no figures. Final version: connection between one-dimensional distributions of annihilating Brownian motions and rea

Scientific paper

10.1214/EJP.v16-942

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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