Optimal paths as correlated random walks

E. Perlsman, S. Havlin

Research output: Contribution to journalArticlepeer-review

7 Scopus citations


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.

Original languageEnglish
Pages (from-to)178-182
Number of pages5
Issue number2
StatePublished - 15 Jan 2006


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