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Phase separation in random cluster models I: uniform upper bounds on local deviation

Abstract:

This is the first in a series of three papers that addresses the behaviour of the droplet that results, in the percolating phase, from conditioning the Fortuin-Kasteleyn planar random cluster model on the presence of an open dual circuit Gamma_0 encircling the origin and enclosing an area of at least (or exactly) n^2. (By the Fortuin-Kasteleyn representation, the model is a close relative of the droplet formed by conditioning the Potts model on an excess of spins of a given type.) We consider...

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Publication status:
Published

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Publisher copy:
10.1007/s00220-011-1370-2

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Institution:
University of Oxford
Division:
MPLS
Department:
Statistics
Role:
Author
Journal:
COMMUNICATIONS IN MATHEMATICAL PHYSICS More from this journal
Volume:
310
Issue:
2
Pages:
455-509
Publication date:
2010-01-10
DOI:
EISSN:
1432-0916
ISSN:
0010-3616
Language:
English
Keywords:
Pubs id:
pubs:204292
UUID:
uuid:8c8bea4c-922c-44d6-8887-6e5ea3fa35c9
Local pid:
pubs:204292
Source identifiers:
204292
Deposit date:
2012-12-19

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