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.
"synopsis" may belong to another edition of this title.
Synopsis
In this book, the author announces the class of problems called "entropy of knots" and gives the overview of existing topological invariants. He constructs statistical models on braids using the representations of Alexander and Jones invariants and puts forward the question of limit distribution of these invariants for randomly generated braids. The relation of highest powers of corresponding algebraic invariants to the Lyapunov exponents of the products of noncommunicative matrices is shown. Also the problem of conditional joint limit distribution 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 the volume, the author also discusses the application of conformal methods for the explicit construction of topological invariants for random walks on multiconnected manifolds. Furthermore the connection of these topological invariants and the monodromy properties of correlation functions of some conformal theories are also discussed.
"About this title" may belong to another edition of this title.
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STATISTICS OF KNOTS AND ENTANGLED RANDOM WALKS
Published by
World Scientific Pub Co Inc, 1996
ISBN 10: 9810225199
ISBN 13: 9789810225193
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Hardcover
Seller: suffolkbooks, Center moriches, NY, U.S.A.
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hardcover. Condition: Very Good. Fast Shipping - Safe and Secure 7 days a week! Seller Inventory # 3TWDDA000FJ5
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Statistics of Knots and Entangled Random Walks
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Hard Cover. Condition: Acceptable. No Jacket. Ex-library with the usual features. The interior is clean and tight. Binding is good. Cover shows light wear and has library label taped on spine. 190 pages. Ex-Library. Seller Inventory # 036970
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Statistics of Knots and Entangled Random Walks
Seller: Free Play Books, NEW HAVEN, CT, U.S.A.
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Hardcover. Condition: Near Fine. Dust Jacket Condition: Fine. 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