Examples of interacting particle systems on \(\mathbb {Z}\) as Pfaffian point processes: annihilating and coalescing random walks
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Publication:1626829
DOI10.1007/S00023-018-0719-XzbMATH Open1410.82015arXiv1507.01843OpenAlexW2811414210MaRDI QIDQ1626829
Author name not available (Why is that?)
Publication date: 21 November 2018
Published in: (Search for Journal in Brave)
Abstract: A class of interacting particle systems on , involving instantaneously annihilating or coalescing nearest neighbour random walks, are shown to be Pfaffan point processes for all deterministic initial conditions. As diffusion limits, explicit Pfaffan kernels are derived for a variety of coalescing and annihilating Brownian systems. For Brownian motions on , depending on the initial conditions, the corresponding kernels are closely related to the bulk and edge scaling limits of the Pfaffan point process for real eigenvalues for the real Ginibre ensemble of random matrices. For Brownian motions on with absorbing or reflected boundary conditions at zero new interesting Pfaffan kernels appear. We illustrate the utility of the Pfaffan 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.
Full work available at URL: https://arxiv.org/abs/1507.01843
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