Survival probability of mutually killing Brownian motions and the O'Connell process
Probability
2012-05-02 v2 Statistical Mechanics
High Energy Physics - Theory
Mathematical Physics
math.MP
Exactly Solvable and Integrable Systems
Abstract
Recently O'Connell introduced an interacting diffusive particle system in order to study a directed polymer model in 1+1 dimensions. The infinitesimal generator of the process is a harmonic transform of the quantum Toda-lattice Hamiltonian by the Whittaker function. As a physical interpretation of this construction, we show that the O'Connell process without drift is realized as a system of mutually killing Brownian motions conditioned that all particles survive forever. When the characteristic length of interaction killing other particles goes to zero, the process is reduced to the noncolliding Brownian motion (the Dyson model).
Keywords
Cite
@article{arxiv.1112.4009,
title = {Survival probability of mutually killing Brownian motions and the O'Connell process},
author = {Makoto Katori},
journal= {arXiv preprint arXiv:1112.4009},
year = {2012}
}
Comments
v2: AMS-LaTeX, 20 pages, 2 figures, minor corrections made for publication in J. Stat. Phys