Probability and Stochastic Analysis - University of Bonn
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Abstract of "Scaling limit for Brownian motions with one-sided collisions"

with Herbert Spohn and Thomas Weiss.

We consider Brownian motions with one-sided collisions, meaning that each particle is reflected at its right neighbour. For a finite number of particles a Sch├╝tz-type formula is derived for the transition probability. We investigate an infinite system with periodic initial configuration, i.e., particles are located at the integer lattice at time zero. The joint distribution of the positions of a finite subset of particles is expressed as a Fredholm determinant with a kernel defining a signed determinantal point process. In the appropriate large time scaling limit, the fluctuations in the particle positions are described by the Airy1 process.

Postscript file: [PS]

PDF file: [PDF]

arXiv: 1306.5095