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I will describe a directed flipping process that underlies the performance of the random edge simplex algorithm. This stochastic process takes place on a one-dimensional lattice whose sites may be either occupied or vacant; an occupied site becomes vacant at a constant rate and simultaneously it causes all sites to the right to change their state. The position of the left-most occupied site defines a front that propagates at a nontrivial velocity. I will show that the front involves a depletion zone with an excess of vacant sites; the total excess increases logarithmically with the distance from the front. Interestingly, the front exhibits rejuvenation --- young fronts are vigorous but old fronts are sluggish. We treat these phenomena using a quasi-static approximation, direct solutions of small systems, and numerical simulations. Host: T-13 |