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On Measures of Average Degree for Lattices

Published online by Cambridge University Press:  07 June 2006

SVEN ERICK ALM
SVEN ERICK ALM
Affiliation:
Department of Mathematics, Uppsala University, PO Box 480, SE-751 06 Uppsala, Sweden (e-mail: [email protected])
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Abstract

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 analysed 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.

Type
Paper
Information
Combinatorics, Probability and Computing , Volume 15 , Issue 4 , July 2006 , pp. 477 - 488
Copyright
2006 Cambridge University Press

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