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 , the winding exponent and other quantities describing the shape of meanders. Received 21 June 1999