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Uniqueness in percolation theory
Author(s) -
Meester R.W.J.
Publication year - 1994
Publication title -
statistica neerlandica
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.52
H-Index - 39
eISSN - 1467-9574
pISSN - 0039-0402
DOI - 10.1111/j.1467-9574.1994.tb01446.x
Subject(s) - uniqueness , mathematical proof , subject (documents) , percolation (cognitive psychology) , percolation theory , mathematics , mathematical economics , calculus (dental) , computer science , combinatorics , topology (electrical circuits) , mathematical analysis , psychology , medicine , geometry , dentistry , neuroscience , library science
The possible uniqueness of the infinite cluster in percolation theory has been a subject of research for more then three decades. A number of important results have been proved in the last eight years and most of the question posed thirty years ago are answered nowadays. In this review paper, I shall give an account on the history of the subject plus recent developments. My goal is not only to mention the main results, but also to give some idea of the methods of proofs which are involved. I also discuss some applications and open problems.