Connectivity properties of continuum percolation processes on R-2

作者: Ph. Blanchard , G. Dell'Antonio , D. Gandolfo , M. Sirugue-Collin

DOI: 10.1023/A:1013157427257

关键词:

摘要: A new approach is introduced in order to estimate the critical parameters of continuous percolation overlapping disks ℝ2 when centres are Poisson distributed. Better insights on relevant near criticality found. Moreover, introducing a suitable connectivity length, model able describe any type geometrical objects ℝ2.

参考文章(13)
L. Chayes, Discontinuity of the Spin-Wave Stiffness in the Two-Dimensional XY Model Communications in Mathematical Physics. ,vol. 197, pp. 623- 640 ,(1998) , 10.1007/S002200050466
H. Satz, Deconfinement and percolation Nuclear Physics. ,vol. 642, pp. 130- 142 ,(1998) , 10.1016/S0375-9474(98)00508-9
V. V. Bazhanov, Yu. G. Stroganov, Hidden symmetry of free fermion model. I. Triangle equation and symmetric parametrization Theoretical and Mathematical Physics. ,vol. 62, pp. 253- 260 ,(1985) , 10.1007/BF01018266
E. J. Garboczi, M. F. Thorpe, M. S. DeVries, A. R. Day, Universal conductivity curve for a plane containing random holes Physical Review A. ,vol. 43, pp. 6473- 6482 ,(1991) , 10.1103/PHYSREVA.43.6473
Shechao Feng, B. I. Halperin, P. N. Sen, Transport properties of continuum systems near the percolation threshold Physical Review B. ,vol. 35, pp. 197- 214 ,(1987) , 10.1103/PHYSREVB.35.197
Harry Kesten, The critical probability of bond percolation on the square lattice equals 1/2 Communications in Mathematical Physics. ,vol. 74, pp. 41- 59 ,(1980) , 10.1007/BF01197577
A. Drory, I. Balberg, U. Alon, B. Berkowitz, Analytic derivation of percolation thresholds in anisotropic systems of permeable objects Physical Review A. ,vol. 43, pp. 6604- 6612 ,(1991) , 10.1103/PHYSREVA.43.6604
U. Alon, A. Drory, I. Balberg, Systematic derivation of percolation thresholds in continuum systems Physical Review A. ,vol. 42, pp. 4634- 4638 ,(1990) , 10.1103/PHYSREVA.42.4634
M. B. Isichenko, Percolation, statistical topography, and transport in random media Reviews of Modern Physics. ,vol. 64, pp. 961- 1043 ,(1992) , 10.1103/REVMODPHYS.64.961
Michael Aizenman, Almut Burchard, Charles M. Newman, David B. Wilson, Scaling limits for minimal and random spanning trees in two dimensions Random Structures and Algorithms. ,vol. 15, pp. 319- 367 ,(1999) , 10.1002/(SICI)1098-2418(199910/12)15:3/4<319::AID-RSA8>3.0.CO;2-G