Pfaffian formulae for one dimensional coalescing and annihilating systems
Tribe, Roger and Zaboronski, Oleg V.. (2011) Pfaffian formulae for one dimensional coalescing and annihilating systems. Electronic Journal of Probability, Vol.16 (No.76). pp. 2080-2103. ISSN 1083-6489
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Official URL: http://dx.doi.org/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.
|Item Type:||Journal Article|
|Subjects:||Q Science > QA Mathematics|
|Divisions:||Faculty of Science > Mathematics|
|Library of Congress Subject Headings (LCSH):||Brownian movements, Pfaffian systems, Point processes|
|Journal or Publication Title:||Electronic Journal of Probability|
|Publisher:||University of Washington. Dept. of Mathematics|
|Official Date:||November 2011|
|Page Range:||pp. 2080-2103|
|Access rights to Published version:||Open Access|
 Arratia. Limiting processes for rescalings of coalescing and annihilating random walks on Zd .
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