Entropy 2008, Volume 10(3), Page 309-318; doi:10.3390/e10030309
Article

Prudent Self-Avoiding Walks

John C. Dethridge email and Anthony J. Guttmann * email ARC Centre of Excellence for Mathematics and Statistics of Complex Systems, Department of Mathematics and Statistics, The University of Melbourne, Victoria 3010, Australia
 E-mails jcd@ms.unimelb.edu.au (J.D.); tonyg@ms.unimelb.edu.au (A.G.) * Author to whom correspondence should be addressed. Received: 17 May 2008 / Accepted: 9 September 2008 / Published: 24 September 2008
PDF Full-text Download PDF Full-Text (164 KB)
This article belongs to the special issue Concepts of Entropy and Their Applications - Papers presented at the Meeting at University of Melbourne, 26 November - 11 December 2007

Abstract: We have produced extended series for prudent self-avoiding walks on the square lattice. These are subsets of self-avoiding walks. We conjecture the exact growth constant and critical exponent for the walks, and show that the (anisotropic) generating function is almost certainly not differentiably-finite.

Keywords: self-avoiding walks; prudent walks; D-finite

To Cite this Article

  • MDPI and ACS Style

    Dethridge, J.C.; Guttmann, A.J. Prudent Self-Avoiding Walks. Entropy 2008, 10, 309-318.

  • AMA Style

    Dethridge J.C., Guttmann A.J. Prudent Self-Avoiding Walks. Entropy. 2008; 10(3):309-318.

  • Chicago/Turabian Style

    Dethridge, John C.; Guttmann, Anthony J.. 2008. "Prudent Self-Avoiding Walks." Entropy 10, no. 3: 309-318.