Survival probability of mutually killing Brownian motions and the O'Connell process

Details Survival probability of mutually killing Brownian motions and the O'Connell process Survival probability of mutually killing Brownian motions and the O'Connell process

2011-12-17

arxiv.org/abs/1112.4009v2

Mathematics

Probability

v2: AMS-LaTeX, 20 pages, 2 figures, minor corrections made for publication in J. Stat. Phys

Scientific paper

10.1007/s10955-012-0472-3

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).

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