A Fleming-Viot particle representation of the Dirichlet Laplacian

We consider. a model with a large number N of particles which move accordin g to independent Brownian motions. A particle which leaves a domain D is ki lled, at the same time, a different particle splits into two particles, For large N, the particle distribution density converges to the normalized hea t equation solution in D with Dirichlet boundary conditions. The stationary distributions converge as N --> infinity to the first eigenfunction of the Laplacian in D with the same boundary conditions.