Sven Erick Alm 2005 J. Phys. A: Math. Gen. 38 2055 doi:10.1088/0305-4470/38/10/001
Sven Erick Alm
Show affiliationsWe give improved upper and lower bounds for the connective constants of self-avoiding walks on a class of lattices, including the Archimedean and Laves lattices. The lower bounds are obtained by using Kesten's method of irreducible bridges, with an appropriate generalization for weakly regular lattices. The upper bounds are obtained as the largest eigenvalue of a certain transfer matrix. The obtained bounds show that, in the studied class of lattices, the connective constant is increasing in the average degree of the lattice. We also discuss an alternative measure of average degree.
05.40.Fb Random walks and Levy flights
02.10.Ox Combinatorics; graph theory
82C41 Dynamics of random walks, random surfaces, lattice animals, etc. (See also 60G50)
Issue 10 (11 March 2005)
Received 14 December 2004, in final form 18 January 2005
Published 23 February 2005
Sven Erick Alm 2005 J. Phys. A: Math. Gen. 38 2055
Jan J Wilkens and Uwe Oelfke 2006 Phys. Med. Biol. 51 3127
Chin-Fei Lee and Paul T. P. Ho 2005 ApJ 624 841
R. T. Edwards et al. 2001 ApJ 560 365
J L Castagner and A R Jones 2003 J. Phys. D: Appl. Phys. 36 2359
Predrag S Krstic and David R Schultz 1999 J. Phys. B: At. Mol. Opt. Phys. 32 3485
H Yan and J Zhang 1996 J. Phys. A: Math. Gen. 29 L413
Yoshio Miura et al 2002 J. Phys.: Condens. Matter 14 L479
N Stüßer et al 2002 J. Phys.: Condens. Matter 14 5161
O Bénichou et al 2005 J. Phys. A: Math. Gen. 38 7205