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Construction of a short path in high dimensional First Passage Percolation
Published 30 Aug 2010 in math.PR | (1008.5069v2)
Abstract: For First Passage Percolation in Zd with large d, we construct a path connecting the origin to {x_1 =1}, whose passage time has optimal order \log d/d. Besides, an improved lower bound for the "diagonal" speed of the cluster combined with a result by Dhar (1988) shows that the limiting shape in FPP with exponential passage times (and thus that of Eden model) is not the euclidian ball in dimension larger than 35.
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