caa a22 4500 445391847 CHVBK 20180317143049.0 cr unu---uuuuu 170323e20110201xx s 000 0 eng 10.1007/s10955-011-0117-y doi (NATIONALLICENCE)springer-10.1007/s10955-011-0117-y Noncolliding Squared Bessel Processes [Elektronische Daten] [Makoto Katori, Hideki Tanemura] We consider a particle system of the squared Bessel processes with index ν>−1 conditioned never to collide with each other, in which if −1<ν<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 ν 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. Springer Science+Business Media, LLC, 2011 Noncolliding diffusion process nationallicence Squared Bessel process nationallicence Fredholm determinants nationallicence Entire functions nationallicence Weierstrass canonical products nationallicence Infinite particle systems nationallicence Katori Makoto Department of Physics, Faculty of Science and Engineering, Chuo University, Kasuga, Bunkyo-ku, 112-8551, Tokyo, Japan aut Tanemura Hideki Department of Mathematics and Informatics, Faculty of Science, Chiba University, 1-33 Yayoi-cho, Inage-ku, 263-8522, Chiba, Japan aut Journal of Statistical Physics Springer US; http://www.springer-ny.com 142/3(2011-02-01), 592-615 0022-4715 142:3<592 2011 142 10955 https://doi.org/10.1007/s10955-011-0117-y text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s10955-011-0117-y text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Katori Makoto Department of Physics, Faculty of Science and Engineering, Chuo University, Kasuga, Bunkyo-ku, 112-8551, Tokyo, Japan aut NATIONALLICENCE 700 1- Tanemura Hideki Department of Mathematics and Informatics, Faculty of Science, Chiba University, 1-33 Yayoi-cho, Inage-ku, 263-8522, Chiba, Japan aut NATIONALLICENCE 773 0- Journal of Statistical Physics Springer US; http://www.springer-ny.com 142/3(2011-02-01), 592-615 0022-4715 142:3<592 2011 142 10955 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer