Volume 77, Number 2, January 2007
|Number of page(s)||4|
|Published online||11 January 2007|
Stability of directed Min-Max optimal paths
Department of Physics, Bar-Ilan University - Ramat-Gan 52900, Israel
Accepted: 17 November 2006
The stability of directed Min-Max optimal paths in cases of change in the random media is studied. Using analytical arguments it is shown that when small perturbations ϵ are applied to the weights of the bonds of the lattice, the probability that the new Min-Max optimal path is different from the original Min-Max optimal path is proportional to , where t is the size of the lattice, and is the longitudinal correlation exponent of the directed percolation model. It is also shown that in a lattice whose bonds are assigned with weights which are near the strong disorder limit, the probability that the directed polymer optimal path is different from the optimal Min-Max path is proportional to , where k is the strength of the disorder. These results are supported by numerical simulations.
PACS: 05.40.-a – Fluctuation phenomena, random processes, noise, and Brownian motion / 05.50.+q – Lattice theory and statistics (Ising, Potts, etc.)
© Europhysics Letters Association, 2007
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