Noncolliding Brownian Motion and Determinantal Processes
| dc.creator | Katori, Makoto | |
| dc.creator | Tanemura, Hideki | |
| dc.date | 2007-05-17 | |
| dc.date | 2007-11-12 | |
| dc.date.accessioned | 2026-07-07T08:45:30Z | |
| dc.date.available | 2026-07-07T08:45:30Z | |
| dc.description | A system of one-dimensional Brownian motions (BMs) conditioned never to collide with each other is realized as (i) Dyson's BM model, which is a process of eigenvalues of hermitian matrix-valued diffusion process in the Gaussian unitary ensemble (GUE), and as (ii) the $h$-transform of absorbing BM in a Weyl chamber, where the harmonic function $h$ is the product of differences of variables (the Vandermonde determinant). The Karlin-McGregor formula gives determinantal expression to the transition probability density of absorbing BM. We show from the Karlin-McGregor formula, if the initial state is in the eigenvalue distribution of GUE, the noncolliding BM is a determinantal process, in the sense that any multitime correlation function is given by a determinant specified by a matrix-kernel. By taking appropriate scaling limits, spatially homogeneous and inhomogeneous infinite determinantal processes are derived. We note that the determinantal processes related with noncolliding particle systems have a feature in common such that the matrix-kernels are expressed using spectral projections of appropriate effective Hamiltonians. On the common structure of matrix-kernels, continuity of processes in time is proved and general property of the determinantal processes is discussed. | |
| dc.description | v3: LaTeX, 43 pages, no figure, minor corrections made for publication in J. Stat. Phys | |
| dc.identifier | https://arxiv.org/abs/0705.2460 | |
| dc.identifier | http://arxiv.org/abs/0705.2460 | |
| dc.identifier | J. Stat. Phys. 129 (2007) 1233-1277 | |
| dc.identifier | doi:10.1007/s10955-007-9421-y | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/142984 | |
| dc.subject | Probability | |
| dc.subject | Statistical Mechanics | |
| dc.subject | High Energy Physics - Theory | |
| dc.subject | Mathematical Physics | |
| dc.subject | Exactly Solvable and Integrable Systems | |
| dc.title | Noncolliding Brownian Motion and Determinantal Processes | |
| dc.type | text |