Front Propagation in Flipping Processes

T. Antal, D. ben-Avraham, E. Ben-Naim, and P.L. Krapivsky

We study a directed flipping process that underlies the performance of the random edge simplex algorithm. In this stochastic process, which takes place on a one-dimensional lattice whose sites may be either occupied or vacant, occupied sites become vacant at a constant rate and simultaneously cause all sites to the right to change their state. This random process exhibits rich phenomenology. First, there is a front, defined by the position of the left-most occupied site, that propagates at a nontrivial velocity. Second, the front involves a depletion zone with an excess of vacant sites. The total excess $\Delta_k$ increases logarithmically, $\Delta_k \simeq \ln k$, with the distance $k$ from the front. Third, the front exhibits rejuvenation --- young fronts are vigorous but old fronts are sluggish. We investigate these phenomena using a quasi-static approximation, direct solutions of small systems, and numerical simulations.


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