2012年1月
Determinantal Process Starting from an Orthogonal Symmetry is a Pfaffian Process
JOURNAL OF STATISTICAL PHYSICS
- 巻
- 146
- 号
- 2
- 開始ページ
- 249
- 終了ページ
- 263
- 記述言語
- 英語
- 掲載種別
- 研究論文(学術雑誌)
- DOI
- 10.1007/s10955-011-0372-y
- 出版者・発行元
- SPRINGER
When the number of particles N is finite, the noncolliding Brownian motion (BM) and the noncolliding squared Bessel process with index nu >-1 (BESQ((nu))) 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 2x2 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, N delta (0), and by the equivalence between the noncolliding BESQ((nu)) and that of the noncolliding squared generalized meander starting from N delta (0).
- リンク情報
- ID情報
-
- DOI : 10.1007/s10955-011-0372-y
- ISSN : 0022-4715
- Web of Science ID : WOS:000298627800001