Scaling limit for Brownian motions with one-sided collisions

Abstract

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 Schütz-type formula is derived for the transition probability. We investigate an infinite system with periodic initial configuration, that is, 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 Airy${}_1$ process.

Published at http://dx.doi.org/10.1214/14-AAP1025 in the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org)

References in corpus (3)

• Fluctuation properties of the TASEP with periodic initial configuration
• Transition between Airy_1 and Airy_2 processes and TASEP fluctuations
• Slow decorrelations in KPZ growth

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• Large Deviations For Sticky Brownian Motions
• Height fluctuations for the stationary KPZ equation
• Brownian Motions with One-Sided Collisions: The Stationary Case
• KPZ universality class and the anchored Toom interface
• Exact solution of interacting particle systems related to random matrices
• Large Deviation Principle for Interacting Brownian Motions
• Triple and Simultaneous Collisions of Competing Brownian Particles