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The Self-Avoiding Walk
Neal Madras, Gordon Slade (Taschenbuch, Englisch)
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Beschreibung
The self-avoiding walk is a mathematical model that has important applications in statistical mechanics and polymer science. In spite of its simple definition—a path on a lattice that does not visit the same site more than once—it is difficult to analyze mathematically. The Self-Avoiding Walk provides the first unified account of the known rigorous results for the self-avoiding walk, with… particular emphasis on its critical behavior. Its goals are to give an account of the current mathematical understanding of the model, to indicate some of the applications of the concept in physics and in chemistry, and to give an introduction to some of the nonrigorous methods used in those fields. Topics covered in the book include: the lace expansion and its application to the self-avoiding walk in more than four dimensions where most issues are now resolved; an introduction to the nonrigorous scaling theory; classical work of Hammersley and others; a new exposition of Kesten’s pattern theorem and its consequences; a discussion of the decay of the two-point function and its relation to probabilistic renewal theory; analysis of Monte Carlo methods that have been used to study the self-avoiding walk; the role of the self-avoiding walk in physical and chemical applications. Methods from combinatorics, probability theory, analysis, and mathematical physics play important roles. The book is highly accessible to both professionals and graduate students in mathematics, physics, and chemistry. 85,59 €
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Technische Daten
Erscheinungsdatum
07.11.2012
Sprache
Englisch
EAN
9781461460244, 9781461460244
Herausgeber
Springer US
Serien- oder Bandtitel
Modern Birkhäuser Classics
Sonderedition
Nein
Autor
Neal Madras, Gordon Slade
Seitenanzahl
427
Einbandart
Taschenbuch
Schlagwörter
Kesten's pattern theorem, lace expansion, polymer science, self-avoiding walk, statistical mechanics, two-point function, combinatorics
Thema-Inhalt
PBT - Wahrscheinlichkeitsrechnung und Statistik
PBWL - Stochastik
PBD - Diskrete Mathematik
PHU - Mathematische Physik
Höhe
235 mm
Breite
15.5 cm
Hersteller: Springer Nature Customer Service Center GmbH, Europaplatz 3, Heidelberg, Deutschland, 69115, ProductSafety@springernature.com
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