A CLASS OF STOCHASTIC EVOLUTIONS THAT SCALE TO THE POROUS-MEDIUM EQUATION

A class of reversible Markov jump processes on a periodic lattice is d escribed and a result about their scaling behavior stated: Under diffu sion scaling, the empirical measure converges to a solution of the por ous medium equation on the d-dimensional torus. The process can be vie wed as a randomly interacting configuration of sticks that evolves thr ough exchanges of stick pieces between nearest neighbors through a zer o-range pressure mechanism, with conservation of total stick length.