A class of stochastic evolutions that scale to the porous medium equation |
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| Authors: | Shui Feng Ian Iscoe Timo Seppäläinen |
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| Institution: | (1) Department of Mathematics and Statistics, McMaster University, L8S 4K1 Hamilton, Ontario, Canada;(2) Present address: Algorithmics, M6J 1C9 Toronto, Ontario, Canada;(3) Department of Mathematics, Iowa State University, 50011-2066 Ames, Iowa |
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| Abstract: | A class of reversible Markov jump processes on a periodic lattice is described and a result about their scaling behavior stated: Under diffusion scaling, the empirical measure converges to a solution of the porous medium equation on thed-dimensional torus. The process can be viewed as a randomly interacting configuration of sticks that evolves through exchanges of stick pieces between nearest neighbors through a zero-range pressure mechanism, with conservation of total stick length. |
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| Keywords: | Porous medium equation hydrodynamic scaling limit |
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