Burdzy, KrzysztofHolyst, RobertMarch, Peter2005-11-302005-11-302000-11Burdzy, K., R. Holyst, & P. March. (2000). A Fleming-Viat particle representation of Dirichlet Laplacian. Communications in Mathematical Physics, 214(3), 679-703.http://hdl.handle.net/1773/2214We consider a model with a large number N of particles which move according to independent Brownian motions. A particle which leaves a domain D is killed; at the same time, a different particle splits into two particles. For large N, the particle distribution density converges to the normalized heat equation solution in D with Dirichlet boundary conditions. The stationary distributions converge as N [goes to infinity] to the first eigenfunction of the Laplacian in D with the same boundary conditions.239079 bytesapplication/pdfen-USBrownian motionparticle distribution densityHeat equationDirichlet boundary conditionseigenfunctionLaplacianArticle