Maximum distributions of bridges of noncolliding Brownian paths
| dc.creator | Kobayashi, Naoki | |
| dc.creator | Izumi, Minami | |
| dc.creator | Katori, Makoto | |
| dc.date | 2008-08-27 | |
| dc.date | 2008-10-03 | |
| dc.date.accessioned | 2026-07-07T10:15:35Z | |
| dc.date.available | 2026-07-07T10:15:35Z | |
| dc.description | The one-dimensional Brownian motion starting from the origin at time $t=0$, conditioned to return to the origin at time $t=1$ and to stay positive during time interval $0 < t < 1$, is called the Bessel bridge with duration 1. We consider the $N$-particle system of such Bessel bridges conditioned never to collide with each other in $0 < t < 1$, which is the continuum limit of the vicious walk model in watermelon configuration with a wall. Distributions of maximum-values of paths attained in the time interval $t \in (0,1)$ are studied to characterize the statistics of random patterns of the repulsive paths on the spatio-temporal plane. For the outermost path, the distribution function of maximum value is exactly determined for general $N$. We show that the present $N$-path system of noncolliding Bessel bridges is realized as the positive-eigenvalue process of the $2N \times 2N$ matrix-valued Brownian bridge in the symmetry class C. Using this fact computer simulations are performed and numerical results on the $N$-dependence of the maximum-value distributions of the inner paths are reported. The present work demonstrates that the extreme-value problems of noncolliding paths are related with the random matrix theory, representation theory of symmetry, and the number theory. | |
| dc.description | REVTeX4, 34 pages, 12 figures, title changed and minor corrections made for publication in Phys. Rev. E | |
| dc.identifier | https://arxiv.org/abs/0808.3635 | |
| dc.identifier | http://arxiv.org/abs/0808.3635 | |
| dc.identifier | Phys. Rev. E 78 (2008) 051102/1-15 | |
| dc.identifier | doi:10.1103/PhysRevE.78.051102 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/173217 | |
| dc.subject | Statistical Mechanics | |
| dc.subject | Soft Condensed Matter | |
| dc.subject | Mathematical Physics | |
| dc.title | Maximum distributions of bridges of noncolliding Brownian paths | |
| dc.type | text |