| Issue |
EPL
Volume 77, Number 2, January 2007
|
|
|---|---|---|
| Article Number | 20003 | |
| Number of page(s) | 4 | |
| Section | General | |
| DOI | https://doi.org/10.1209/0295-5075/77/20003 | |
| Published online | 11 January 2007 | |
Stability of directed Min-Max optimal paths
Department of Physics, Bar-Ilan University - Ramat-Gan 52900, Israel
Received:
18
July
2006
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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