Construction of a Short Path in High-dimensional First Passage Percolation
نویسنده
چکیده
For first passage percolation in Zd with large d, we construct a path connecting the origin to {x1 = 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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