Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
1155379 | Stochastic Processes and their Applications | 2016 | 12 Pages |
Abstract
We consider first-passage percolation on the d dimensional cubic lattice for dâ¥2; that is, we assign independently to each edge e a nonnegative random weight te with a common distribution and consider the induced random graph distance (the passage time), T(x,y). It is known that for each xâZd, μ(x)=limnT(0,nx)/n exists and that 0â¤ET(0,x)âμ(x)â¤Câxâ11/2logâxâ1 under the condition Eeαte<â for some α>0. By combining tools from concentration of measure with Alexander's methods, we show how such bounds can be extended to te's with distributions that have only low moments. For such edge-weights, we obtain an improved bound C(âxâ1logâxâ1)1/2 and bounds on the rate of convergence to the limit shape.
Related Topics
Physical Sciences and Engineering
Mathematics
Mathematics (General)
Authors
Michael Damron, Naoki Kubota,