Determinantal Process Starting from an Orthogonal Symmetry is a Pfaffian Process |
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Authors: | Makoto Katori |
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Institution: | 1. Department of Physics, Faculty of Science and Engineering, Chuo University, Kasuga, Bunkyo-ku, Tokyo, 112-8551, Japan
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Abstract: | When the number of particles N is finite, the noncolliding Brownian motion (BM) and the noncolliding squared Bessel process with index ν>−1 (BESQ(ν)) are determinantal processes for arbitrary fixed initial configurations. In the present paper we prove that, if initial configurations
are distributed with orthogonal symmetry, they are Pfaffian processes in the sense that any multitime correlation functions
are expressed by Pfaffians. The 2×2 skew-symmetric matrix-valued correlation kernels of the Pfaffians processes are explicitly
obtained by the equivalence between the noncolliding BM and an appropriate dilatation of a time reversal of the temporally
inhomogeneous version of noncolliding BM with finite duration in which all particles start from the origin, Nδ
0, and by the equivalence between the noncolliding BESQ(ν) and that of the noncolliding squared generalized meander starting from Nδ
0. |
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Keywords: | |
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