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


Authors: Takashi Hara and Gordon Slade
Journal: Bull. Amer. Math. Soc. 25 (1991), 417-423
MSC (1985): Primary 82A67, 82A25, 60K35; Secondary 82A51
DOI: https://doi.org/10.1090/S0273-0979-1991-16085-4
MathSciNet review: 1093059
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  • 1. D. C. Brydges and T. Spencer, Self-avoiding walk in 5 or more dimensions, Comm. Math. Phys. 97 (1985), 125-148. MR 782962
  • 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. MR 849206
  • 3. A. J. Guttmann, Bounds on connective constants for self-avoiding walks, J. Phys. A 16 (1983), 2233-2238. MR 713186
  • 4. J. M. Hammersley, Percolation processes.II, Connective constants. Proc. Cambridge Philos. Soc. 53 (1957), 642-645. MR 91568
  • 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. MR 139535
  • 6. T. Hara, Mean field critical behaviour for correlation length for percolation in high dimensions, Probab. Theory Related Fields 86 (1990), 337-385. MR 1069285
  • 7. T. Hara and G. Slade, Self-avoiding walk in five or more dimensions. I, The critical behaviour, preprint, 1991. MR 1093059
  • 8. T. Hara and G. Slade, Self-avoiding walk in five or more dimensions. II, Convergence of the lace expansion, preprint, 1991. MR 1093059
  • 9. H. Kesten, On the number of self-avoiding walks. II, J. Math. Phys. 5 (1964), 1128-1137. MR 166845
  • 10. G. Lawler, The infinite self-avoiding walk in high dimensions, Ann. Probab. 17 (1989), 1367-1376. MR 1048931
  • 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. MR 939485
  • 12. B. Nienhuis, Critical behavior of two-dimensional spin models and charge asymmetry in the Coulomb gas, J. Statist. Phys. 34 (1984), 731-761. MR 751711
  • 13. G. Slade, The diffusion of self-avoiding random walk in high dimensions, Comm. Math. Phys. 110 (1987), 661-683. MR 895223
  • 14. G. Slade, Convergence of self-avoiding random walk to Brownian motion in high dimensions, J. Phys. A 21 (1988), L417-L420. MR 951038
  • 15. G. Slade, The scaling limit of self-avoiding random walk in high dimensions, Ann. Probab. 17 (1989), 91-107. MR 972773

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DOI: https://doi.org/10.1090/S0273-0979-1991-16085-4

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