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A phase transition for the heights of a fragmentation tree
Author(s) -
Joseph Adrien
Publication year - 2011
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.20340
Subject(s) - cardinality (data modeling) , fragmentation (computing) , mathematics , partition (number theory) , homogeneous , phase transition , random tree , tree (set theory) , combinatorics , discrete mathematics , branching process , statistical physics , computer science , physics , quantum mechanics , data mining , motion planning , artificial intelligence , robot , operating system
We provide information about the asymptotic regimes for a homogeneous fragmentation of a finite set. We establish a phase transition for the asymptotic behavior of the shattering times, defined as the first instants when all the blocks of the partition process have cardinality less than a fixed integer. Our results may be applied to the study of certain random split trees. © 2010 Wiley Periodicals, Inc. Random Struct. Alg., 39, 247‐274, 2011