Percolation on random Johnson-Mehl tessellations and related models

被引：12

作者：

Bollobas, Bela

Riordan, Oliver

机构：

[1] Univ Cambridge, Dept Math & Math Stat, Cambridge CB3 0WB, England

[2] Univ Memphis, Dept Math Sci, Memphis, TN 38152 USA

来源：

PROBABILITY THEORY AND RELATED FIELDS | 2008年 / 140卷 / 3-4期

基金：

美国国家科学基金会;

关键词：

D O I：

10.1007/s00440-007-0066-1

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

We make use of the recent proof that the critical probability for percolation on random Voronoi tessellations is 1/2 to prove the corresponding result for random Johnson-Mehl tessellations, as well as for two-dimensional slices of higher-dimensional Voronoi tessellations. Surprisingly, the proof is a little simpler for these more complicated models.

引用

页码：319 / 343

页数：25

共 27 条

[1] Kinetics of phase change I - General theory [J].

Avrami, M .

JOURNAL OF CHEMICAL PHYSICS, 1939, 7 (12) :1103-1112

[2]

Avrami M., 1940, J CHEM PHYS, V8, P212, DOI 10.1063/1.1750631

[3]

Bollobas B., 2006, PERCOLATION

[4] The critical probability for random Voronoi percolation in the plane is 1/2 [J].

Bollobas, Bela ;

Riordan, Oliver .

PROBABILITY THEORY AND RELATED FIELDS, 2006, 136 (03) :417-468

[5]

Chiu SN, 1997, ANN APPL PROBAB, V7, P802

[6]

Delesse A, 1848, ANN MINES, V13, P379

[7]

Dirichlet G.L., 1850, J. fur die reine und angewandte Mathematik (Crelles J.), V1850, P209, DOI DOI 10.1515/CRLL.1850.40.209

[8] RANDOM AND COOPERATIVE SEQUENTIAL ADSORPTION [J].

EVANS, JW .

REVIEWS OF MODERN PHYSICS, 1993, 65 (04) :1281-1329

[9] The Johnson-Mehl-Avrami-Kolmogorov model: A brief review [J].

Fanfoni, M ;

Tomellini, M .

NUOVO CIMENTO DELLA SOCIETA ITALIANA DI FISICA D-CONDENSED MATTER ATOMIC MOLECULAR AND CHEMICAL PHYSICS FLUIDS PLASMAS BIOPHYSICS, 1998, 20 (7-8) :1171-1182

[10] Film growth viewed as stochastic dot processes [J].

Fanfoni, M ;

Tomellini, M .

JOURNAL OF PHYSICS-CONDENSED MATTER, 2005, 17 (17) :R571-R605

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