Quasirandomness in Graphs
نویسندگان
چکیده
Jim Propp’s rotor router model is a simple deterministic analogue of a random walk. Instead of distributing chips randomly, it serves the neighbors in a fixed order. We analyze the difference between Propp machine and random walk on the infinite twodimensional grid. We show that, independent of the starting configuration, at each time, the number of chips on each vertex deviates from the expected number of chips in the random walk model by at most a constant c, which is 7.83 for clockwise rotor sequences and 7.28 otherwise. This is the first paper which demonstrates that the order in which the neighbors are served makes a difference.
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عنوان ژورنال:
- Electronic Notes in Discrete Mathematics
دوره 25 شماره
صفحات -
تاریخ انتشار 2006