Construction of a short path in high dimensional First Passage Percolation
Construction of a short path in high dimensional First Passage Percolation
For First Passage Percolation in Z^d 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 …