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

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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
Subjects:	Q Science > QA Mathematics
Divisions:	Faculty of Science > Computer Science Faculty of Science > Statistics
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:	Date Event March 2003 Published
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
Funder:	Engineering and Physical Sciences Research Council (EPSRC)
Grant number:	GR/M75785 (EPSRC)

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