Derandomization of Euclidean Random Walks

We consider the problem of derandomizing random walks in the Euclidean space i¾?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.

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