Abstract:
We 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→∞ to the first eigenfunction of the Laplacian in D with the same boundary conditions.
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Received: 11 November 1999 / Accepted: 19 May 2000
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Burdzy, K., Hołyst, R. & March, P. A Fleming–Viot Particle Representation¶of the Dirichlet Laplacian. Commun. Math. Phys. 214, 679–703 (2000). https://doi.org/10.1007/s002200000294
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DOI: https://doi.org/10.1007/s002200000294