Abstract
We consider the problem of derandomizing random walks in the Euclidean space 
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/n is the desired precision of the simulation.
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Binder, I., Braverman, M. (2007). Derandomization of Euclidean Random Walks. In: Charikar, M., Jansen, K., Reingold, O., Rolim, J.D.P. (eds) Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques. APPROX RANDOM 2007 2007. Lecture Notes in Computer Science, vol 4627. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-74208-1_26
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DOI: https://doi.org/10.1007/978-3-540-74208-1_26
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