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We give a deterministicÕ(log n)-space algorithm for approximately solving linear systems given by Laplacians of undirected graphs, and consequently also approximating hitting times, commute times, and escape probabilities for undirected graphs. Previously, such systems were known to be solvable by randomized algorithms using O(log n) space (Doron, Le Gall, and Ta-Shma, 2017) and hence by deterministic algorithms using O(log 3/2 n) space (Saks and Zhou, FOCS 1995 and JCSS 1999). Our algorithmdoi:10.1109/focs.2017.79 dblp:conf/focs/MurtaghRSV17 fatcat:hw3sxqd5wvgnljea3yrdqb54oy