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Available in print format 		Bulletin of the American Mathematical Society
Bulletin of the American Mathematical Society
ISSN 1088-9485(e) ISSN 0273-0979(p)

     

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:

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M. Aizenman, Geometric analysis of $ {\phi ^4}$ fields and Ising models, Comm. Math. Phys. 86 (1982), 1-48. MR 678000 (84f:81078)

[2]
P. Billingsley, Convergence of probability measures, Wiley, New York, 1968. MR 0233396 (38:1718)

[3]
D. C. Brydges and T. C. Spencer, Self-avoiding walk in 5 or more dimensions, Comm. Math. Phys. 97 (1985), 125-148. MR 782962 (86h:82056)

[4]
P. J. Flory, Principles of polymer chemistry, Cornell Univ. Press, Ithaca, NY, 1953.

[5]
J. Fröhlich, On the triviality of $ \lambda \phi _d^4$ theories and the approach to the critical point in $ d \geq 4$ dimensions, Nuclear Phys. B 200 (1982), 281-296. MR 643591 (83h:81046)

[6]
J. M. Hammersley and K. W. Morton, Poor man's Monte Carlo, J. Roy. Statist. Soc. Ser. B 16 (1954), 23-38. MR 0064475 (16:287i)

[7]
T. Hara and G. Slade, Self-avoiding walk in five or more dimensions, I: The critical behavior, Comm. Math. Phys. 147 (1992), 101-136. MR 1171762 (93j:82032)

[8]
-, The lace expansion for self-avoiding walk in five or more dimensions, Rev. Math. Phys. 4 (1992), 235-327. MR 1174248 (93j:82033)

[9]
M. Kac, Probability and related topics in physical sciences, Interscience, New York, 1959. MR 0102849 (21:1635)

[10]
W. Kuhn, Über die Gestalt fadenförmiger Moleküle in Lösungen, Kolloid-Zeitschrift 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. 47 (1987), 573-595. MR 894408 (88h:82055)

[12]
E. W. Montroll, Markoff chains and excluded volume effect in polymer chains, J. Chem. Phys. 18 (1950), 734-743. MR 0036468 (12:114e)

[13]
G. Slade, The diffusion of self-avoiding random walk in high dimensions, Comm. Math. Phys. 110 (1987), 661-683. MR 895223 (88h:82017)

[14]
-, Convergence of self-avoiding random walk to Brownian motion in high dimensions, J. Phys. A 21 (1988), L417-L420. MR 951038 (89d:60127)

[15]
-, The scaling limit of self-avoiding random walk in high dimensions, Ann. Probab. 17 (1989), 91-107. MR 972773 (90f:60125)

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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