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Phase Separation in Random Cluster Models III: Circuit Regularity

Abstract:

We study the droplet that results from conditioning the subcritical Fortuin-Kasteleyn random cluster model on the presence of an open circuit Γ encircling the origin and enclosing an area of at least (or exactly) n 2. In this paper, we prove that the resulting circuit is highly regular: we define a notion of a regeneration site in such a way that, for any such site v∈Γ, the circuit Γ cuts through the radial line segment through v only at v. We show that, provided that ...

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Publication status:
Published

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Publisher copy:
10.1007/s10955-010-0081-y

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Institution:
University of Oxford
Division:
MPLS
Department:
Statistics
Role:
Author
Journal:
JOURNAL OF STATISTICAL PHYSICS More from this journal
Volume:
142
Issue:
2
Pages:
229-276
Publication date:
2011-01-01
DOI:
EISSN:
1572-9613
ISSN:
0022-4715
Language:
English
Pubs id:
pubs:118165
UUID:
uuid:8ba5ad6c-f2e5-4f7f-9326-154006f5007d
Local pid:
pubs:118165
Source identifiers:
118165
Deposit date:
2012-12-19

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