
STATISTICAL TOPOLOGY OF RANDOM WALKSSerguei Nechaev (Personal webpage)Laboratoire de physique thÃ©orique et de modÃ¨les statistiques, Universite ParisSud
We discuss few interlinked topics in statistics of entangled random walks: conformal methods in topology of random path on multipunctured plane, random walks on graphs and groups (including braid groups), "matrixvalued" Brownian bridges and random walks in Lobachevsky geometry. We explain how all these subjects help in understanding topology and fractal structure of strongly collapsed unknotted ring polymer chain.
References:
[1] S. Nechaev. Statistics of knots and entangled random walks,Lectures presented at Les Houches. In: Summer School"Topological Aspects of Low Dimensional Systems", July 731,1998. NATO Advanced Study Institute, session LXIX: EDP Sciences;Springer, 1999. 