Connectivity properties of Mandelbrot's percolation process
Publication
, Journal Article
Chayes, JT; Chayes, L; Durrett, R
Published in: Probability Theory and Related Fields
March 1, 1988
In 1974, Mandelbrot introduced a process in [0, 1]2 which he called "canonical curdling" and later used in this book(s) on fractals to generate self-similar random sets with Hausdorff dimension D∈(0,2). In this paper we will study the connectivity or "percolation" properties of these sets, proving all of the claims he made in Sect. 23 of the "Fractal Geometry of Nature" and a new one that he did not anticipate: There is a probability pc∈(0,1) so that if p
Duke Scholars
Published In
Probability Theory and Related Fields
DOI
EISSN
1432-2064
ISSN
0178-8051
Publication Date
March 1, 1988
Volume
77
Issue
3
Start / End Page
307 / 324
Related Subject Headings
- Statistics & Probability
- 4905 Statistics
- 4904 Pure mathematics
- 0104 Statistics
- 0102 Applied Mathematics
- 0101 Pure Mathematics
Citation
APA
Chicago
ICMJE
MLA
NLM
Chayes, J. T., Chayes, L., & Durrett, R. (1988). Connectivity properties of Mandelbrot's percolation process. Probability Theory and Related Fields, 77(3), 307–324. https://doi.org/10.1007/BF00319291
Chayes, J. T., L. Chayes, and R. Durrett. “Connectivity properties of Mandelbrot's percolation process.” Probability Theory and Related Fields 77, no. 3 (March 1, 1988): 307–24. https://doi.org/10.1007/BF00319291.
Chayes JT, Chayes L, Durrett R. Connectivity properties of Mandelbrot's percolation process. Probability Theory and Related Fields. 1988 Mar 1;77(3):307–24.
Chayes, J. T., et al. “Connectivity properties of Mandelbrot's percolation process.” Probability Theory and Related Fields, vol. 77, no. 3, Mar. 1988, pp. 307–24. Scopus, doi:10.1007/BF00319291.
Chayes JT, Chayes L, Durrett R. Connectivity properties of Mandelbrot's percolation process. Probability Theory and Related Fields. 1988 Mar 1;77(3):307–324.
Published In
Probability Theory and Related Fields
DOI
EISSN
1432-2064
ISSN
0178-8051
Publication Date
March 1, 1988
Volume
77
Issue
3
Start / End Page
307 / 324
Related Subject Headings
- Statistics & Probability
- 4905 Statistics
- 4904 Pure mathematics
- 0104 Statistics
- 0102 Applied Mathematics
- 0101 Pure Mathematics