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On the duality between coalescing Brownian particles and the heat equation driven by Fisher-Wright noise. (English) Zbl 1111.60073

Summary: This paper concerns the Markov process duality between the one-dimensional heat equation driven by Fisher-Wright white noise and slowly coalescing Brownian particles. A representation is found for the law of the solution \(x\to U(t,x)\) to the stochastic partial differential equation, at a fixed time, in terms of a labelled system of such particles.

MSC:

60K35 Interacting random processes; statistical mechanics type models; percolation theory
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