Premium
Percolation of arbitrary words in one dimension
Author(s) -
Grimmett Geoffrey R.,
Liggett Thomas M.,
Richthammer Thomas
Publication year - 2010
Publication title -
random structures and algorithms
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.314
H-Index - 69
eISSN - 1098-2418
pISSN - 1042-9832
DOI - 10.1002/rsa.20312
Subject(s) - bernoulli's principle , percolation (cognitive psychology) , dimension (graph theory) , sequence (biology) , mathematics , percolation threshold , word (group theory) , type (biology) , range (aeronautics) , countable set , bernoulli distribution , continuum percolation theory , discrete mathematics , combinatorics , statistical physics , percolation critical exponents , random variable , physics , statistics , psychology , engineering , quantum mechanics , aerospace engineering , electrical resistivity and conductivity , genetics , biology , geometry , thermodynamics , neuroscience , ecology
We consider a type of long‐range percolation problem on the positive integers, motivated by earlier work of others on the appearance of (in)finite words within a site percolation model. The main issue is whether a given infinite binary word appears within an iid Bernoulli sequence at locations that satisfy certain constraints. We settle the issue in some cases, and we provide partial results in others. © 2010 Wiley Periodicals, Inc. Random Struct. Alg., 2010