Configurational transition in a Fleming-Viot-type model and probabilistic interpretation of Laplacian eigenfunctions

Details Configurational transition in a Fleming-Viot-type model and probabilistic interpretation of Laplacian eigenfunctions Configurational transition in a Fleming-Viot-type model and probabilistic interpretation of Laplacian eigenfunctions

1996-03-08

arxiv.org/abs/cond-mat/9603064v1

Physics

Condensed Matter

17 pages (Plain TeX) 4 figures on request (burdzy@math.washington.edu). to be published in J.Phys.A

Scientific paper

10.1088/0305-4470/29/11/004

We analyze and simulate a two dimensional Brownian multi-type particle system with death and branching (birth) depending on the position of particles of different types. The system is confined in the two dimensional box, whose boundaries act as the sink of Brownian particles. The branching rate matches the death rate so that the total number of particles is kept constant. In the case of m types of particles in the rectangular box of size a,b and elongated shape $a\gg b$ we observe that the stationary distribution of particles corresponds to the m-th Laplacian eigenfunction. For smaller elongations $a>b$ we find a configurational transition to a new limiting distribution. The ratio a/b for which the transition occurs is related to the value of the m-th eigenvalue of the Laplacian with rectangular boundaries.

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