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Random threshold growth dynamics
Author(s) -
Bohman Tom,
Gravner Janko
Publication year - 1999
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/(sici)1098-2418(199908)15:1<93::aid-rsa4>3.0.co;2-k
Subject(s) - property (philosophy) , mathematics , convergence (economics) , set (abstract data type) , point (geometry) , statistical physics , combinatorics , discrete mathematics , computer science , physics , geometry , economics , philosophy , epistemology , programming language , economic growth
A site in Z becomes occupied with a certain probability as soon as it sees at least a threshold number of already occupied sites in its neighborhood. Such randomly growing sets have the following regularity property: a large fully occupied set exists within a fixed distance (which does not increase with time) of every occupied point. This property suffices to prove convergence to an asymptotic shape. ©1999 John Wiley & Sons, Inc. Random Struct. Alg., 15: 93–111, 1999