First passage percolation in many dimensions

Dhar, D. (1988) First passage percolation in many dimensions Physics Letters A, 130 (4-5). pp. 308-310. ISSN 0375-9601

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We consider first passage percolation on a d-dimensional hypercubical lattice. The passage time for each bond is an independent exponentially distributed random variable with mean l. For large separations, the limiting ratio of expected minimum passage time between two points along an axis and their separation is a constant μd, and we show that limd→∞ μd/ln d = ½.

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