## 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

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## 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/BF00319291Chayes, 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