Math @ Duke

Publications [#243445] of Richard T. Durrett
Papers Published
 Chayes, JT; Chayes, L; Durrett, R, Connectivity properties of Mandelbrot's percolation process,
Probability Theory and Related Fields, vol. 77 no. 3
(March, 1988),
pp. 307324, Springer Nature America, Inc, ISSN 01788051 [doi]
(last updated on 2019/04/22)
Abstract: 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 selfsimilar 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


dept@math.duke.edu
ph: 919.660.2800
fax: 919.660.2821
 
Mathematics Department
Duke University, Box 90320
Durham, NC 277080320

