Book Review
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MathSciNet review:
1568077
Full text of review:
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Book Information:
Author:
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.
Michael Aizenman, Geometric analysis of $\varphi ^{4}$ fields and Ising models. I, II, Comm. Math. Phys. 86 (1982), no. 1, 1–48. MR 678000
Patrick Billingsley, Convergence of probability measures, John Wiley & Sons, Inc., New York-London-Sydney, 1968. MR 0233396
David Brydges and Thomas Spencer, Self-avoiding walk in $5$ or more dimensions, Comm. Math. Phys. 97 (1985), no. 1-2, 125–148. MR 782962
[4] P. J. Flory, Principles of polymer chemistry, Cornell Univ. Press, Ithaca, NY, 1953.
Jürg Fröhlich, On the triviality of $\lambda \varphi ^{4}_{d}$ theories and the approach to the critical point in $d{>atop (—)}4$ dimensions, Nuclear Phys. B 200 (1982), no. 2, 281–296. MR 643591, DOI 10.1016/0550-3213(82)90088-8
J. M. Hammersley and K. W. Morton, Poor man’s Monte Carlo, J. Roy. Statist. Soc. Ser. B 16 (1954), 23–38; discussion 61–75. MR 64475
Takashi Hara and Gordon Slade, Self-avoiding walk in five or more dimensions. I. The critical behaviour, Comm. Math. Phys. 147 (1992), no. 1, 101–136. MR 1171762
Takashi Hara and Gordon Slade, The lace expansion for self-avoiding walk in five or more dimensions, Rev. Math. Phys. 4 (1992), no. 2, 235–327. MR 1174248, DOI 10.1142/S0129055X9200008X
Mark Kac, Probability and related topics in physical sciences, Lectures in Applied Mathematics (Proceedings of the Summer Seminar, Boulder, Colorado, vol. 1957, Interscience Publishers, London-New York, 1959. With special lectures by G. E. Uhlenbeck, A. R. Hibbs, and B. van der Pol. MR 0102849
[10] W. Kuhn, Über die Gestalt fadenförmiger Moleküle in Lösungen, Kolloid-Zeitschrift 68 (1934), 2-15.
Neal Madras and Alan D. Sokal, Nonergodicity of local, length-conserving Monte Carlo algorithms for the self-avoiding walk, J. Statist. Phys. 47 (1987), no. 3-4, 573–595. MR 894408, DOI 10.1007/BF01007527
Elliott W. Montroll, Markoff chains and excluded volume effect in polymer chains, J. Chem. Phys. 18 (1950), 734–743. MR 36468, DOI 10.1063/1.1747735
Gordon Slade, The diffusion of self-avoiding random walk in high dimensions, Comm. Math. Phys. 110 (1987), no. 4, 661–683. MR 895223
Gordon Slade, Convergence of self-avoiding random walk to Brownian motion in high dimensions, J. Phys. A 21 (1988), no. 7, L417–L420. MR 951038
Gordon Slade, The scaling limit of self-avoiding random walk in high dimensions, Ann. Probab. 17 (1989), no. 1, 91–107. MR 972773
- [1]
- M. Aizenman, Geometric analysis of
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
theories and the approach to the critical point in 
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)
Review Information:
Reviewer:
Harry Kesten
Journal:
Bull. Amer. Math. Soc.
30 (1994), 104-108
DOI:
https://doi.org/10.1090/S0273-0979-1994-00441-0
