2011年2月
Noncolliding Squared Bessel Processes
JOURNAL OF STATISTICAL PHYSICS
- ,
- 巻
- 142
- 号
- 3
- 開始ページ
- 592
- 終了ページ
- 615
- 記述言語
- 英語
- 掲載種別
- 研究論文(学術雑誌)
- DOI
- 10.1007/s10955-011-0117-y
- 出版者・発行元
- SPRINGER
We consider a particle system of the squared Bessel processes with index nu >-1 conditioned never to collide with each other, in which if -1 <nu < 0 the origin is assumed to be reflecting. When the number of particles is finite, we prove for any fixed initial configuration that this noncolliding diffusion process is determinantal in the sense that any multitime correlation function is given by a determinant with a continuous kernel called the correlation kernel. When the number of particles is infinite, we give sufficient conditions for initial configurations so that the system is well defined. There the process with an infinite number of particles is determinantal and the correlation kernel is expressed using an entire function represented by the Weierstrass canonical product, whose zeros on the positive part of the real axis are given by the particle-positions in the initial configuration. From the class of infinite-particle initial configurations satisfying our conditions, we report one example in detail, which is a fixed configuration such that every point of the square of positive zero of the Bessel function J (nu) is occupied by one particle. The process starting from this initial configuration shows a relaxation phenomenon converging to the stationary process, which is determinantal with the extended Bessel kernel, in the long-term limit.
- リンク情報
- ID情報
-
- DOI : 10.1007/s10955-011-0117-y
- ISSN : 0022-4715
- Web of Science ID : WOS:000286990900007