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Stochastic Loewner evolution and Dyson's circular ensembles

Abstract:

Stochastic Loewner evolution (SLEκ) has been introduced as a description of the continuum limit of cluster boundaries in two-dimensional critical systems. We show that the problem of N radial SLEs in the unit disc is equivalent to Dyson's Brownian motion on the boundary of the disc, with parameter β = 4/κ. As a result, various equilibrium critical models give realizations of circular ensembles with β different from the classical values of 1, 2 and 4 which correspond to symmetry classes of ran...

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Publication status:
Published

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Publisher copy:
10.1088/0305-4470/36/24/101

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Journal:
JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL More from this journal
Volume:
36
Issue:
24
Pages:
L379-L386
Publication date:
2003-06-20
DOI:
EISSN:
1361-6447
ISSN:
0305-4470
Language:
English
Pubs id:
pubs:240729
UUID:
uuid:aab5a66d-8433-49ad-a0ce-8a283d104a55
Local pid:
pubs:240729
Source identifiers:
240729
Deposit date:
2012-12-19

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