Derandomization of Euclidean Random Walks

Authors:
Ilia Binder;Mark Braverman
Affiliations:
Dept. of Mathematics, University of Toronto,;Dept. of Computer Science, University of Toronto,
Venue:
APPROX '07/RANDOM '07 Proceedings of the 10th International Workshop on Approximation and the 11th International Workshop on Randomization, and Combinatorial Optimization. Algorithms and Techniques
Year:
2007

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Abstract

We consider the problem of derandomizing random walks in the Euclidean space 茂戮驴k. We show that for k= 2, and in some cases in higher dimensions, such walks can be simulated in Logspace using only poly-logarithmically many truly random bits.As a corollary, we show that the Dirichlet Problem can be deterministically simulated in space $O(\log n\sqrt{\log\log n})$, where 1/nis the desired precision of the simulation.