2013/06/30 by Patrik L. Ferrari, Herbert Spohn, Thomas Weiss +1
Mathematics · Physics and Astronomy · #Brownian excursion #Brownian motion #Diffusion process #Fredholm determinant #Geometric Brownian motion #Geometry #Half-integer #Integer lattice #Kernel (algebra) #Lattice (music) #Limit (mathematics) #Mathematical analysis #Mathematics #Physics #Point process #Pure mathematics #Quantum mechanics #Random Matrices and Applications #Scaling #Scaling limit #Statistical physics #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #math-ph #math.MP #math.PR
paper · pdf · doi:10.1214/14-aap1025
published as Annals of Applied Probability 2015, Vol. 25, No. 3, 1349-1382 · 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)
openalex publication_date 2015/03/23 · arxiv created 2015/04/22 · arxiv updated 2015/04/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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 Airy1 process.