Derandomization of Euclidean Random Walks

We consider the problem of derandomizing random walks in the Euclidean space Rk . 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 random walk can be deterministically simulated in space O(logn √ loglog n), where 1/n is the desired precision of the simulation.

• Type: Conference
• Year: 2007
• Where: APPROX
• Authors: Ilia Binder, Mark Braverman
• Keywords: Algorithms, APPROX 2007, Euclidean Space Rk, Random Bits, Random Walk