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Book Review
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Book Information
Author(s):
Neal Madras and Gordon Slade
Title:
The self-avoiding walk
Additional book information:
Birkh\"auser, Boston, 1993, xiv+425 pp., US$64.50. ISBN 3-7643-3589-0
References:
- [1]
- M. Aizenman, Geometric analysis of $\phi ^4$ fields and Ising models, Comm. Math. Phys. \textbf{86} (1982), 1--48.
- [2]
- P. Billingsley, Convergence of probability measures, Wiley, New York, 1968.
- [3]
- D. C. Brydges and T. C. Spencer, Self-avoiding walk in $5$ or more dimensions, Comm. Math. Phys. \textbf{97} (1985), 125--148.
- [4]
- P. J. Flory, Principles of polymer chemistry, Cornell Univ. Press, Ithaca, NY, 1953.
- [5]
- J. Fr\"ohlich, On the triviality of $\lambda \phi _d^4$ theories and the approach to the critical point in $d\ge 4$ dimensions, Nuclear Phys. \textbf{B 200} (1982), 281--296.
- [6]
- J. M. Hammersley and K. W. Morton, Poor man{\rm '}s Monte Carlo, J. Roy. Statist. Soc. Ser. \textbf{B 16} (1954), 23--38.
- [7]
- T. Hara and G. Slade, Self-avoiding walk in five or more dimensions, {\rm I:} The critical behavior, Comm. Math. Phys. \textbf{147} (1992), 101--136.
- [8]
- T. Hara and G. Slade, The lace expansion for self-avoiding walk in five or more dimensions, Rev. Math. Phys. \textbf{4} (1992), 235--327.
- [9]
- M. Kac, Probability and related topics in physical sciences, Interscience, New York, 1959.
- [10]
- W. Kuhn, \"Uber die Gestalt fadenf\"ormiger Molek\"ule in L\"osungen, Kolloid-Zeitschrift \textbf{68} (1934), 2--15.
- [11]
- N. Madras and A. D. Sokal, Nonergodicity of local, lengthconserving Monte Carlo algorithms for the self-avoiding walk, J. Statist. Phys. \textbf{47} (1987), 573--595.
- [12]
- E. W. Montroll, Markoff chains and excluded volume effect in polymer chains, J. Chem. Phys. \textbf{18} (1950), 734--743.
- [13]
- G. Slade, The diffusion of self-avoiding random walk in high dimensions, Comm. Math. Phys. \textbf{110} (1987), 661--683.
- [14]
- G. Slade, Convergence of self-avoiding random walk to Brownian motion in high dimensions, J. Phys. A \textbf{21} (1988), L417--L420.
- [15]
- G. Slade, The scaling limit of self-avoiding random walk in high dimensions, Ann. Probab. \textbf{17} (1989), 91--107.
Additional Information:
Reviewer(s):
Harry
Kesten
Review Information:
Journal:
Bull. Amer. Math. Soc.
30
(1994),
104-108.
DOI:
10.1090/S0273-0979-1994-00441-0
PII:
S 0273-0979(1994)00441-0
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