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On Measures of Average Degree for Lattices
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Mathematical Statistics.
2006 (English)In: Combinatorics, Probability and Computing, Vol. 15, no 4, 477-488 p.Article in journal (Refereed) Published
Abstract [en]

The usual definition of average degree for a non-regular lattice has the disadvantage that it takes the same value for many lattices with clearly different connectivity. We introduce an alternative definition of average degree, which better separates different lattices.

These measures are compared on a class of lattices and are analyzed using a Markov chain describing a random walk on the lattice. Using the new measure, we conjecture the order of both the critical probabilities for bond percolation and the connective constants for self-avoiding walks on these lattices.

Place, publisher, year, edition, pages
2006. Vol. 15, no 4, 477-488 p.
Keyword [en]
average degree, lattices
National Category
Probability Theory and Statistics
URN: urn:nbn:se:uu:diva-22348DOI: 10.1017/S0963548305007418ISI: 000238673600001OAI: oai:DiVA.org:uu-22348DiVA: diva2:50121
Available from: 2007-01-16 Created: 2007-01-16 Last updated: 2016-09-07Bibliographically approved

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Alm, Sven Erick
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