 |
Journal articles
An Optimal Algorithm to Generate Extendable Self-Avoiding Walks in Arbitrary Dimension
Abstract : A self-avoiding walk (SAW) is extendable [10,13] if it can be extended into an infinite SAW. We give a simple proof that, for every lattice, extendable SAWs admit the same connective constant that the general SAWs and we give an optimal linear algorithm to generate random extendable SAWs. Our algorithm can generate every extendable SAW in dimension 2. For dimension d > 2, it generates only a subset of the extendable SAWs. We conjecture that this subset is " large " and has the same connective constant that the extendable SAWs. Our algorithm produces a kinetic distribution of the extendable SAWs, for which the critical exponent ν ≈ .57 for d = 2, .51 for d = 3 and .50 for d = 4, 5, 6.
Cited literature [18 references]
https://hal.archives-ouvertes.fr/hal-01790908
Contributor : Pascal Préa <>
Submitted on : Monday, May 14, 2018 - 10:36:22 AM
Last modification on : Monday, January 13, 2020 - 9:06:31 AM
Long-term archiving on: : Tuesday, September 25, 2018 - 7:52:42 PM
Contributor : Pascal Préa <>
Submitted on : Monday, May 14, 2018 - 10:36:22 AM
Last modification on : Monday, January 13, 2020 - 9:06:31 AM
Long-term archiving on: : Tuesday, September 25, 2018 - 7:52:42 PM
File
Extensible-SAW_PP-MR-FB.pdf
Files produced by the author(s)