Statistics of knots and entangled random walks
| dc.creator | Nechaev, Sergei | |
| dc.date | 1998-12-11 | |
| dc.date.accessioned | 2026-07-07T03:12:22Z | |
| dc.date.available | 2026-07-07T03:12:22Z | |
| dc.description | 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 the probability of a trivial knot formation on the lattice using the Kauffman algebraic invariants and show the connection of this problem with the thermodynamic properties of 2D disordered Potts model; (ii) We investigate the limit behavior of random walks in multi-connected spaces and on non-commutative groups related to the knot theory. We discuss the application of the above mentioned problems in statistical physics of polymer chains. On the basis of non-commutative probability theory we derive some new results in statistical physics of entangled polymer chains which unite rigorous mathematical facts with more intuitive physical arguments. | |
| dc.description | Extended version of lectures presented at Les Houches 1998 summer school "Topological Aspects of Low Dimensional Systems", July 7 - 31, 1998; revtex, 79 pages, 16 eps-figures | |
| dc.identifier | https://arxiv.org/abs/cond-mat/9812205 | |
| dc.identifier | http://arxiv.org/abs/cond-mat/9812205 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/28883 | |
| dc.subject | Statistical Mechanics | |
| dc.subject | Soft Condensed Matter | |
| dc.subject | Probability | |
| dc.title | Statistics of knots and entangled random walks | |
| dc.type | text |