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Linear cover time is exponentially unlikelyMathematical Physics & Probability
|Speaker: ||Ben Morris, UC Davis|
|Location: ||1147 MSB|
|Start time: ||Wed, Jan 26 2011, 4:10PM|
We show that the probability that a simple random walk covers a finite, bounded degree graph in linear time is exponentially small.
More precisely, for every D and C, there exists a=a(D,C)>0 such that for any graph G, with n vertices and maximal degree D, the probability that a simple random walk, started anywhere in G, will visit every vertex of G in its first Cn steps is at most exp(-an).
Joint work with Itai Benjamini and Ori Gurel-Gurevich.