A Monte-Carlo study of meanders

We study the statistics of meanders, i.e. configurations of a road crossing a river through n bridges, and possibly winding around the source, as a toy model for compact folding of polymers. We introduce a Monte-Carlo method which allows us to simulate large meanders up to n = 400. By performing large n extrapolations, we give asymptotic estimates of the connectivity per bridge R = 3.5018(3), the configuration exponent gamma = 2.056(10), the winding exponent v = 0.518(2) and other quantities describing the shape of meanders.