Department of Computer Science | Institute of Theoretical Computer Science | CADMO

Prof. Emo Welzl and Prof. Bernd Gärtner

Mittagsseminar Talk Information |

**Date and Time**: Thursday, March 02, 2006, 12:15 pm

**Duration**: This information is not available in the database

**Location**: This information is not available in the database

**Speaker**: Joshua Cooper (Courant Inst., NYU and ETH Zürich)

Jim Propp's P-machine, also known as the `rotor-router model' is a simple deterministic process that simulates a random walk on a graph. Instead of distributing chips to randomly chosen neighbors, it serves the neighbors in a fixed order.

We investigate how well this process simulates a random walk. For the
graph being the infinite path, we show that, independent of the starting
configuration, at each time and on each vertex, the number of chips on
this vertex deviates from the expected number of chips in the random
walk model by at most a constant c_{1}, which is approximately 2.29. For
intervals of length L, this improves to a difference of O(log L), for
the L_{2} average of a contiguous set of intervals even to O(√{log L}).

Joint work with Benjamin Doerr, Joel Spencer, and Gábor Tardos.

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