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A connective constant for loop-erased self-avoiding random walk

Published online by Cambridge University Press:  14 July 2016

Gregory F. Lawler
Gregory F. Lawler*
Affiliation:
Duke University
*
∗ Postal address: Department of Mathematics, Duke University, Durham, NC 27706, U.S.A. Research supported by National Science Foundation grant MCS-8002758.
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Abstract

A ‘connective constant' is defined for self-avoiding random walk derived by erasing loops from simple random walk. For d ≧ 5, it is shown that this distribution on n-step self-avoiding paths approaches a uniform distribution in a weak sense.

Keywords

SELF-AVOIDING WALKCONNECTIVE CONSTANT
Type
Research Papers
Information
Journal of Applied Probability , Volume 20 , Issue 2 , June 1983 , pp. 264 - 276
Copyright
Copyright © Applied Probability Trust 1983 

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References

[1] Billingsley, P. (1965) Ergodic Theory and Information. Wiley, New York.Google Scholar
[2] Hammersley, J. and Morton, K. W. (1954) Poor man's Monte Carlo. J. R. Statist. Soc. B 16, 23–28.Google Scholar
[3] Kesten, H. (1964) On the number of self-avoiding walks II. J. Math. Phys. 5, 1128–1137.Google Scholar
[4] Lawler, G. F. (1980) A self-avoiding random walk. Duke Math. J. 47, 655–696.Google Scholar