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 PDE, at a fixed time, in terms of a labelled system of such particles.
"On the Duality between Coalescing Brownian Particles and the Heat Equation Driven by Fisher-Wright Noise." Electron. Commun. Probab. 10 136 - 145, 2005. https://doi.org/10.1214/ECP.v10-1143