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Stability properties of a flow process in graphs
Author(s) -
Van Den Berg J.,
Meester R. W. J.
Publication year - 1991
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.3240020308
Subject(s) - stability (learning theory) , flow (mathematics) , process (computing) , mathematics , finite set , combinatorics , discrete mathematics , computer science , mathematical analysis , geometry , machine learning , operating system
We study a flow process in infinite graphs where vertices with large resources tend to attract resources from neighbors. The initial resources are random. An interesting question is whether in each finite region all motion stops after a finite time. Under certain assumptions, we prove that this is true. For some other cases, we prove a weaker stability result. We pay attention mostly to the case of Z 2 , but several results can be easily generalized to Z d .