%P R2029-R2032
%T Optimal path and directed percolation
%V 53
%I American Physical Society
%X An efficient transfer matrix technique is introduced to study directed optimal paths in two and three dimensions. The roughness exponent ? is 0.6325?0.0007 for the two-dimensional case and ?=0.555?0.008 for the three-dimensional one, in agreement with the recent conjecture ?=??/??, where ?? and ?? are the correlation length exponents of directed percolation. Exactly solvable examples are also analyzed.
%D 1996
%L eprints1183
%K PACS: 05.40.+j, 02.50.-r

%A Paolo Rios
%A Guido Caldarelli
%A Amos Maritan
%A Flavio Seno
%R 10.1103/PhysRevE.53.R2029
%N 3
%J Physical Review E