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Ising models and multiresolution quad-trees
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Kendall, W. S. and Wilson, Roland (2003) Ising models and multiresolution quad-trees. Advances in Applied Probability, Vol.35 (No.1). pp. 96-122. doi:10.1239/aap/1046366101 ISSN 0001-8678.
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Official URL: http://dx.doi.org/10.1239/aap/1046366101
Abstract
We study percolation and Ising models defined on generalizations of quad-trees used in multiresolution image analysis. These can be viewed as trees for which each mother vertex has 2(d) daughter vertices, and for which daughter vertices are linked together in d-dimensional Euclidean configurations. Retention probabilities and interaction strengths differ according to whether the relevant bond is between mother and daughter or between neighbours. Bounds are established which locate phase transitions and show the existence of a coexistence phase for the percolation model. Results are extended to the corresponding Ising model using the Fortuin-Kasteleyn random-cluster representation.
Item Type: | Journal Article | ||||
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Subjects: | Q Science > QA Mathematics | ||||
Divisions: | Faculty of Science, Engineering and Medicine > Science > Computer Science Faculty of Science, Engineering and Medicine > Science > Statistics |
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Library of Congress Subject Headings (LCSH): | Percolation (Statistical physics), Ising model, Image analysis | ||||
Journal or Publication Title: | Advances in Applied Probability | ||||
Publisher: | Applied Probability Trust | ||||
ISSN: | 0001-8678 | ||||
Official Date: | March 2003 | ||||
Dates: |
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Volume: | Vol.35 | ||||
Number: | No.1 | ||||
Number of Pages: | 27 | ||||
Page Range: | pp. 96-122 | ||||
DOI: | 10.1239/aap/1046366101 | ||||
Status: | Peer Reviewed | ||||
Publication Status: | Published | ||||
Access rights to Published version: | Restricted or Subscription Access | ||||
Date of first compliant deposit: | 5 December 2015 | ||||
Date of first compliant Open Access: | 5 December 2015 | ||||
Funder: | Engineering and Physical Sciences Research Council (EPSRC) | ||||
Grant number: | GR/M75785 (EPSRC) |
Data sourced from Thomson Reuters' Web of Knowledge
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