MARC Record from harvard_bibliographic_metadata

LEADER: 04821nam a22004815a 4500
001 014157778-9
005 20141003190225.0
008 110928s1996 xxu| o ||0| 0|eng d
020 $a9781461241324
020 $a9780817638917 (ebk.)
020 $a9781461241324
020 $a9780817638917
024 7 $a10.1007/978-1-4612-4132-4$2doi
035 $a(Springer)9781461241324
040 $aSpringer
050 4 $aQA273.A1-274.9
050 4 $aQA274-274.9
072 7 $aMAT029000$2bisacsh
072 7 $aPBT$2bicssc
072 7 $aPBWL$2bicssc
082 04 $a519.2$223
100 1 $aMadras, Neal,$eauthor.
245 14 $aThe Self-Avoiding Walk /$cby Neal Madras, Gordon Slade.
264 1 $aBoston, MA :$bBirkhäuser Boston,$c1996.
300 $aXIV, 427 p.$bonline resource.
336 $atext$btxt$2rdacontent
337 $acomputer$bc$2rdamedia
338 $aonline resource$bcr$2rdacarrier
347 $atext file$bPDF$2rda
490 1 $aProbability and Its Applications
505 0 $a1 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 -- 5.6 Notes -- 6 Above four dimensions -- 6.1 Overview of the results -- 6.2 Convergence of the lace expansion -- 6.3 Fractional derivatives -- 6.4 cn and the mean-square displacement --
505 0 $a6.5 Correlation length and infrared bound -- 6.6 Convergence to Brownian motion -- 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 -- 9.3 Static methods -- 9.4 Length-conserving dynamic methods -- 9.5 Variable-length dynamic methods -- 9.6 Fixed-endpoint methods -- 9.7 Proofs -- 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 --
505 0 $aB Proof of the renewal theorem -- C Tables of exact enumerations -- Notation.
520 $aA self-avoiding walk is a path on a lattice that does not visit the same site more than once. In spite of this simple definition, many of the most basic questions about this model are difficult to resolve in a mathematically rigorous fashion. In particular, we do not know much about how far an n­ step self-avoiding walk typically travels from its starting point, or even how many such walks there are. These and other important questions about the self-avoiding walk remain unsolved in the rigorous mathematical sense, although the physics and chemistry communities have reached consensus on the answers by a variety of nonrigorous methods, including computer simulations. But there has been progress among mathematicians as well, much of it in the last decade, and the primary goal of this book is to give an account of the current state of the art as far as rigorous results are concerned. A second goal of this book is to discuss some of the applications of the self-avoiding walk in physics and chemistry, and to describe some of the nonrigorous methods used in those fields. The model originated in chem­ istry several decades ago as a model for long-chain polymer molecules. Since then it has become an important model in statistical physics, as it exhibits critical behaviour analogous to that occurring in the Ising model and related systems such as percolation.
650 10 $aMathematics.
650 0 $aDistribution (Probability theory)
650 0 $aMathematics.
650 24 $aProbability Theory and Stochastic Processes.
700 1 $aSlade, Gordon,$eauthor.
776 08 $iPrinted edition:$z9780817638917
830 0 $aProbability and Its Applications.
988 $a20140910
906 $0VEN