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Bulletin (New Series) of the American Mathematical Society

Critical behaviour of self-avoiding walk in five or more dimensions

Takashi Hara and Gordon Slade

Source: Bull. Amer. Math. Soc. (N.S.) Volume 25, Number 2 (1991), 417-423.

Primary Subjects: 82A67, 82A25, 60K35
Secondary Subjects: 82A51

Full-text: Open access

Links and Identifiers

Permanent link to this document: http://projecteuclid.org/euclid.bams/1183657191
Mathematical Reviews number (MathSciNet): MR1093059
Zentralblatt MATH identifier: 0728.60103

References

1. D. C. Brydges and T. Spencer, Self-avoiding walk in 5 or more dimensions, Comm. Math. Phys. 97 (1985), 125-148.
Zentralblatt MATH: 0575.60099
Mathematical Reviews (MathSciNet): MR782962
2. J. T. Chayes and L. Chayes, Ornstein-Zernike behavior for self-avoiding walks at all noncritical temperatures Comm. Math. Phys. 105 (1986), 221-238.
Mathematical Reviews (MathSciNet): MR849206
3. A. J. Guttmann, Bounds on connective constants for self-avoiding walks, J. Phys. A 16 (1983), 2233-2238.
Mathematical Reviews (MathSciNet): MR713186
4. J. M. Hammersley, Percolation processes.II, Connective constants. Proc. Cambridge Philos. Soc. 53 (1957), 642-645.
Zentralblatt MATH: 0091.13902
Mathematical Reviews (MathSciNet): MR91568
5. J. M. Hammersley and D. J. A. Welsh, Further results on the rate of convergence to the connective constant of the hypercubical lattice, Quart. J. Math. Oxford (2) 13 (1962), 108-110.
Zentralblatt MATH: 0123.00304
Mathematical Reviews (MathSciNet): MR139535
6. T. Hara, Mean field critical behaviour for correlation length for percolation in high dimensions, Probab. Theory Related Fields 86 (1990), 337-385.
Zentralblatt MATH: 0685.60102
Mathematical Reviews (MathSciNet): MR1069285
7. T. Hara and G. Slade, Self-avoiding walk in five or more dimensions. I, The critical behaviour, preprint, 1991.
Zentralblatt MATH: 0755.60053
Mathematical Reviews (MathSciNet): MR1093059
8. T. Hara and G. Slade, Self-avoiding walk in five or more dimensions. II, Convergence of the lace expansion, preprint, 1991.
Mathematical Reviews (MathSciNet): MR1093059
9. H. Kesten, On the number of self-avoiding walks. II, J. Math. Phys. 5 (1964), 1128-1137.
Zentralblatt MATH: 0161.37402
Mathematical Reviews (MathSciNet): MR166845
10. G. Lawler, The infinite self-avoiding walk in high dimensions, Ann. Probab. 17 (1989), 1367-1376.
Zentralblatt MATH: 0691.60062
Mathematical Reviews (MathSciNet): MR1048931
11. N. Madras and A. D. Sokal, The pivot algorithm: A highly efficient Monte Carlo method for the self-avoiding walk, J. Statist. Phys. 50 (1988), 109-186.
Zentralblatt MATH: 1084.82503
Mathematical Reviews (MathSciNet): MR939485
12. B. Nienhuis, Critical behavior of two-dimensional spin models and charge asymmetry in the Coulomb gas, J. Statist. Phys. 34 (1984), 731-761.
Zentralblatt MATH: 0595.76071
Mathematical Reviews (MathSciNet): MR751711
13. G. Slade, The diffusion of self-avoiding random walk in high dimensions, Comm. Math. Phys. 110 (1987), 661-683.
Zentralblatt MATH: 0628.60073
Mathematical Reviews (MathSciNet): MR895223
14. G. Slade, Convergence of self-avoiding random walk to Brownian motion in high dimensions, J. Phys. A 21 (1988), L417-L420.
Zentralblatt MATH: 0653.60061
Mathematical Reviews (MathSciNet): MR951038
15. G. Slade, The scaling limit of self-avoiding random walk in high dimensions, Ann. Probab. 17 (1989), 91-107.
Zentralblatt MATH: 0664.60069
Mathematical Reviews (MathSciNet): MR972773

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Bulletin (New Series) of the American Mathematical Society

Bulletin (New Series) of the American Mathematical Society