Statistics of Knots and Entangled Random Walks

Nechaev, S. K.

ISBN 10: 9810225199 / ISBN 13: 9789810225193

Published by World Scientific, 1996

About this Item

Glossy illustrated paper boards. 8.75 x 6.5 inches, xiv, 190 pp. Burgundy leatherette boards lettered in gilt at spine. Slight paper residue from dust jacket to the surface of boards where leatherette is somewhat tacky, no internal markings. Illustrated jacket. Near Fine in Fine dust jacket. In mylar sleeve.

Seller Inventory # 5572

Bibliographic Details

• Title: Statistics of Knots and Entangled Random Walks
• Publisher: World Scientific
• Publication Date: 1996
• Language: English
• ISBN 10: 9810225199
• ISBN 13: 9789810225193
• Binding: Hardcover
• Condition: Near Fine
• Dust Jacket Condition: Fine

About this title

Synopsis

In this book, the author announces the class of problems called "entropy of knots" and gives an overview of modern physical applications of existing topological invariants.

He constructs statistical models on knot diagrams and braids using the representations of Jones-Kauffman and Alexander invariants and puts forward the question of limit distribution of these invariants for randomly generated knots. The relation of powers of corresponding algebraic invariants to the Lyapunov exponents of the products of noncommutative matrices is described. Also the problem of conditional joint limit distributions for "brownian bridges" on braids is discussed. Special cases of noncommutative groups PSL(2,R), PSL(2,Z) and braid groups are considered in detail.

In this volume, the author also discusses the application of conformal methods for explicit construction of topological invariants for random walks on multiconnected manifolds. The construction of these topological invariants and the monodromy properties of correlation function of some conformal theories are also discussed. The author also considers the physical applications of "knot entropy" problem in various physical systems, focussing on polymers.