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cond-mat.stat-mech2004
Topological percolation on a square lattice
S. K. Nechaev, O. A. Vasilyev
We investigate the formation of an infinite cluster of entangled threads in a (2+1)-dimensional system. We demonstrate that topological percolation belongs to the universality clas…
cond-mat.stat-mech2002
Topological correlations in trivial knots: new arguments in support of the crumpled polymer globule
Sergei Nechaev, Oleg Vasilyev
We prove the fractal crumpled structure of collapsed unknotted polymer ring. In this state the polymer chain forms a system of densely packed folds, mutually separated in all scale…
cond-mat.stat-mech1998
Statistics of knots and entangled random walks
Sergei Nechaev
The lectures review the state of affairs in modern branch of mathematical physics called probabilistic topology. In particular we consider the following problems: (i) We estimate t…