Europhys. Lett.
Volume 73, Number 2, January 2006
Page(s) 178 - 182
Section General
Published online 09 December 2005
Europhys. Lett., 73 (2), pp. 178-182 (2006)
DOI: 10.1209/epl/i2005-10382-9

Optimal paths as correlated random walks

E. Perlsman and S. Havlin

Department of Physics, Bar-Ilan University - Ramat-Gan 52900, Israel

received 31 July 2005; accepted in final form 22 November 2005
published online 9 December 2005

A numerical study of optimal paths in the directed polymer model shows that the paths are similar to correlated random walks. It is shown that when a directed optimal path of length t is divided into 3 segments whose length is t/3, the correlation between the transversal movements along the first and last path segments is independent of the path length t. It is also shown that the transversal correlations along optimal paths decrease as the paths approach their endpoints. The numerical results obtained for optimal paths in 1+4 dimensions are qualitatively similar to those obtained for optimal paths in lower dimensions, and the data supplies a strong numerical indication that 1+4 is not the upper critical dimension of this model, and of the associated KPZ equation.

05.40.-a - Fluctuation phenomena, random processes, noise, and Brownian motion.
05.50.+q - Lattice theory and statistics (Ising, Potts, etc.).

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