Stability of directed Min-Max optimal pathsE. Perlsman and S. Havlin
Department of Physics, Bar-Ilan University - Ramat-Gan 52900, Israel
received 18 July 2006; accepted in final form 17 November 2006; published January 2007
published online 11 January 2007
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 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.
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