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A technique to approximate heat diffusion on Riemannian manifolds is presented. We provide a numerical way to approximate the solution to the heat equation by using the idea of random walks of particles, governed by a continuous-time Markov chain, where the transition rates of the Markov chain are characterized by the distances between nodes on a given grid with non-equally placed nodes. The emphasis...
In order to approximate heat diffusion in two dimensions, we view diffusion processes as the random motion of particles and model the behavior of each particle with a continuous-time Markov chain. The infinitesimal generator of each Markov chain is characterized by the distances between lattice points imposed on a given two-dimensional surface. We derive requirements for the mean and the covariance...
A probabilistic model for the diffusion of heat on one-dimensional spaces is developed. Specifically, grid points are arbitrarily placed on the real line and the heat particles are assumed to jump between these grid points in continuous time. This random walk by the heat particles is represented by a continuous-time Markov chain and state-transition intensities depends on the underlying, possibly...
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