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Examples of interacting particle systems on Z as Pfaffian point processes : annihilating and coalescing random walks
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Garrod, Barnaby, Poplavskyi, Mihail, Tribe, Roger and Zaboronski, Oleg V. (2018) Examples of interacting particle systems on Z as Pfaffian point processes : annihilating and coalescing random walks. Annales Henri Poincare, 19 (12). pp. 3635-3662. doi:10.1007/s00023-018-0719-x ISSN 1424-0637.
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Official URL: https://doi.org/10.1007/s00023-018-0719-x
Abstract
A class of interacting particle systems on Z, involving instantaneously annihilating or coalescing nearest neighbour random walks, are shown to be Pfaffian point processes for all deterministic initial conditions. As diffusion limits, explicit Pfaffian kernels are derived for a variety of coalescing and annihilating Brownian systems. For Brownian motions on R, depending on the initial conditions, the corresponding kernels are closely related to the bulk and edge scaling limits of the Pfaffian point process for real eigenvalues for the real Ginibre ensemble of random matrices. For Brownian motions on R+ with absorbing or reflected boundary conditions at zero, new interesting Pfaffian kernels appear. We illustrate the utility of the Pfaffian structure by determining the extreme statistics of the rightmost particle for the purely annihilating Brownian motions, and also computing the probability of overcrowded regions for all models.
Item Type: | Journal Article | ||||||||||||
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Subjects: | Q Science > QA Mathematics | ||||||||||||
Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||||||||||
Library of Congress Subject Headings (LCSH): | Random walks (Mathematics), Pfaffian systems, Brownian motion processes | ||||||||||||
Journal or Publication Title: | Annales Henri Poincare | ||||||||||||
Publisher: | Springer Basel AG | ||||||||||||
ISSN: | 1424-0637 | ||||||||||||
Official Date: | December 2018 | ||||||||||||
Dates: |
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Volume: | 19 | ||||||||||||
Number: | 12 | ||||||||||||
Page Range: | pp. 3635-3662 | ||||||||||||
DOI: | 10.1007/s00023-018-0719-x | ||||||||||||
Status: | Peer Reviewed | ||||||||||||
Publication Status: | Published | ||||||||||||
Access rights to Published version: | Open Access (Creative Commons) | ||||||||||||
Date of first compliant deposit: | 20 July 2018 | ||||||||||||
Date of first compliant Open Access: | 17 September 2018 | ||||||||||||
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