Entanglement in percolation

Proceedings of the London Mathematical Society

Volumn 81, Issue 2, 2000, Pages 485-512

  Grimmett, Geoffrey R ^a   Holroyd, Alexander E ^a  

^a UNIVERSITY OF CAMBRIDGE   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0000513990     PISSN: 00246115     EISSN: None     Source Type: Journal    
DOI: 10.1112/S0024611500012521     Document Type: Article

References (16)

1. M. AIZENMAN, J. T. CHAYES, L. CHAYES, J. FRÖHLICH and L. RUSSO, 'On a sharp transition from area law to perimeter law in a system of random surfaces', Comm. Math. Phys. 92 (1983) 19-69.
2. M. AIZENMAN and G. GRIMMETT, 'Strict monotonicity for critical points in percolation and ferromagnetic models', J. Statist. Phys. 63 (1991) 817-835.
3. M. BROWN, 'Locally flat imbeddings of topological manifolds', Ann. of Math. 75 (1962) 331-341.
4. R. M. BURTON and M. KEANE, 'Density and uniqueness in percolation', Comm. Math. Phys. 121 (1989) 501-505.
5. J.-D. DEUSCHEL and A. PISZTORA, 'Surface order large deviations for high-density percolation', Probab. Theory Related Fields 104 (1996) 467-482.
6. Y. DIAO and E. J. JANSE VAN RENSBURG, 'Percolation of linked circles', Topology and geometry in polymer science (ed. S. G. Whittington, D. W. Sumners and T. Lodge), IMA Volumes in Mathematics and its Applications 103 (Springer, New York, 1998) 79-88.
7. G. R. GRIMMETT, 'Percolation and disordered systems', École d'Été de Probabilités de Saint Flour XXVI-1996 (ed. P. Bernard), Lecture Notes in Mathematics 1665 (Springer, New York, 1997) 153-300.
8. G. R. GRIMMETT, Percolation, 2nd edn (Springer, Berlin, 1999).
9. G. R. GRIMMETT and J. M. MARSTRAND, 'The supercritical phase of percolation is well behaved', Proc. Roy. Soc. London. Ser. A 430 (1990) 439-457.
10. A. E. HOLROYD, 'Existence and uniqueness of infinite components in generic rigidity percolation', Ann. Appl. Probab. 8 (1998) 944-973.
11. A. E. HOLROYD, 'Existence of a phase transition in entanglement percolation', Math. Proc. Cambridge Philos. Soc. to appear.
12. T. KANTOR and G. N. HASSOLD, 'Topological entanglements in the percolation problem', Phys Rev. Lett. 60 (1988) 1457-1460.
13. K. KURATOWSKI, Topology, Vol. II (PWN, Warsaw, 1968).
14. W. B. R. LICKORISH, An introduction to knot theory (Springer, New York, 1997).
15. T. M. LIGGETT, R. H. SCHONMANN and A. M. STACEY, 'Domination by product measures' Ann Probab. 25 (1997) 71-95.
16. C. P. ROURKE and B. J. SANDERSON, Introduction to piecewise-linear topology (Springer, Berlin, 1972).