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The Self-Avoiding Walk

Aus der Reihe Probability and Its Applications (duplicate)
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Beschreibung

Produktdetails

Einband

Taschenbuch

Erscheinungsdatum

28.08.1996

Verlag

Birkhäuser Boston

Seitenzahl

427

Maße (L/B/H)

23,3/15,5/2,5 cm

Gewicht

666 g

Auflage

1996

Sprache

Englisch

ISBN

978-0-8176-3891-7

Beschreibung

Rezension

"An excellent introduction for graduate students and professional probabilists... The best place to find a self-contained exposition of lace expansion."


—Bulletin of the AMS


"As a carefully written and carefully referenced exposition of an intriguing topic...this monograph is strongly recommended."


—Monatshefte Mathematik


"In this book, the reader will find basically everything there is to know about rigorous mathematical results on self-avoiding walks... It is nicely written and should be read by mathematical physicists and probabilists interested in applications to natural sciences."


—Belgian Mathematical Society


"This is the first book on self-avoiding random walk and a very good one."


—SIAM Review


"An excellent book that should be on the shelf of anyone doing work at the intersection of probability and critical phenomena... The best results about the SAW can still be found here."


--Annals of Probability

Produktdetails

Einband

Taschenbuch

Erscheinungsdatum

28.08.1996

Verlag

Birkhäuser Boston

Seitenzahl

427

Maße (L/B/H)

23,3/15,5/2,5 cm

Gewicht

666 g

Auflage

1996

Sprache

Englisch

ISBN

978-0-8176-3891-7

Herstelleradresse

Springer Nature c/o IBS
Benzstrasse 21
48619 Heek
DE

Email: GPSR Kontakt

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  • Produktbild: The Self-Avoiding Walk
  • Produktbild: The Self-Avoiding Walk
  • 1 Introduction.- 1.1 The basic questions.- 1.2 The connective constant.- 1.3 Generating functions.- 1.4 Critical exponents.- 1.5 The bubble condition.- 1.6 Notes.- 2 Scaling, polymers and spins.- 2.1 Scaling theory.- 2.2 Polymers.- 2.3 The N ? 0 limit.- 2.4 Notes.- 3 Some combinatorial bounds.- 3.1 The Hammersley-Welsh method.- 3.2 Self-avoiding polygons.- 3.3 Kesten’s bound on cN.- 3.4 Notes.- 4 Decay of the two-point function.- 4.1 Properties of the mass.- 4.2 Bridges and renewal theory.- 4.3 Separation of the masses.- 4.4 Ornstein-Zernike decay of GZ(0, x).- 4.5 Notes.- 5 The lace expansion.- 5.1 Inclusion-exclusion.- 5.2 Algebraic derivation of the lace expansion.- 5.3 Example: the memory-two walk.- 5.4 Bounds on the lace expansion.- 5.5 Other models.- 5.5.1 Lattice trees and animals.- 5.5.2 Percolation.- 5.6 Notes.- 6 Above four dimensions.- 6.1 Overview of the results.- 6.2 Convergence of the lace expansion.- 6.2.1 Preliminaries.- 6.2.2 The convergence proof.- 6.2.3 Proof of Theorem 6.1.2.- 6.3 Fractional derivatives.- 6.4 cn and the mean-square displacement.- 6.4.1 Fractional derivatives of the two-point function.- 6.4.2 Proof of Theorem 6.1.1.- 6.5 Correlation length and infrared bound.- 6.5.1 The correlation length.- 6.5.2 The infrared bound.- 6.6 Convergence to Brownian motion.- 6.6.1 The scaling limit of the endpoint.- 6.6.2 The finite-dimensional distributions.- 6.6.3 Tightness.- 6.7 The infinite self-avoiding walk.- 6.8 The bound on cn(0,x).- 6.9 Notes.- 7 Pattern theorems.- 7.1 Patterns.- 7.2 Kesten’s Pattern Theorem.- 7.3 The main ratio limit theorem.- 7.4 End patterns.- 7.5 Notes.- 8 Polygons, slabs, bridges and knots.- 8.1 Bounds for the critical exponent ?sing.- 8.2 Walks with geometrical constraints.- 8.3 The infinite bridge.- 8.4 Knots in self-avoiding polygons.- 8.5 Notes.- 9 Analysis of Monte Carlo methods.- 9.1 Fundamentals and basic examples.- 9.2 Statistical considerations.- 9.2.1 Curve-fitting and linear regression.- 9.2.2 Autocorrelation times: statistical theory.- 9.2.3 Autocorrelation times: spectral theory and rigorous bounds.- 9.3 Static methods.- 9.3.1 Early methods: strides and biased sampling.- 9.3.2 Dimerization.- 9.3.3 Enrichment.- 9.4 Length-conserving dynamic methods.- 9.4.1 Local algorithms.- 9.4.2 The “slithering snake” algorithm.- 9.4.3 The pivot algorithm.- 9.5 Variable-length dynamic methods.- 9.5.1 The Berretti-Sokal algorithm.- 9.5.2 The join-and-cut algorithm.- 9.6 Fixed-endpoint methods.- 9.6.1 The BFACF algorithm.- 9.6.2 Nonlocal methods.- 9.7 Proofs.- 9.7.1 Autocorrelation times.- 9.7.2 Local algorithms.- 9.7.3 The pivot algorithm.- 9.7.4 Fixed-endpoint methods.- 9.8 Notes.- 10 Related topics.- 10.1 Weak self-avoidance and the Edwards model.- 10.2 Loop-erased random walk.- 10.3 Intersections of random walks.- 10.4 The “myopic” or “true” self-avoiding walk.- A Random walk.- B Proof of the renewal theorem.- C Tables of exact enumerations.- Notation.