Self-avoiding walks on the lattice ℤ² with the 8-neighbourhood system

Andrzej Chydziński, and Bogdan Smołka. "Self-avoiding walks on the lattice ℤ² with the 8-neighbourhood system." Applicationes Mathematicae 28.2 (2001): 169-180. <http://eudml.org/doc/279713>.

@article{AndrzejChydziński2001,
abstract = {This paper deals with the properties of self-avoiding walks defined on the lattice with the 8-neighbourhood system. We compute the number of walks, bridges and mean-square displacement for N=1 through 13 (N is the number of steps of the self-avoiding walk). We also estimate the connective constant and critical exponents, and study finite memory and generating functions. We show applications of this kind of walk. In addition, we compute upper bounds for the number of walks and the connective constant.},
author = {Andrzej Chydziński, Bogdan Smołka},
journal = {Applicationes Mathematicae},
keywords = {self-avoiding walk; lattice with the 8-neighbourhood system; connective constant; critical exponent; mean-square displacement},
language = {eng},
number = {2},
pages = {169-180},
title = {Self-avoiding walks on the lattice ℤ² with the 8-neighbourhood system},
url = {http://eudml.org/doc/279713},
volume = {28},
year = {2001},
}

TY - JOUR
AU - Andrzej Chydziński
AU - Bogdan Smołka
TI - Self-avoiding walks on the lattice ℤ² with the 8-neighbourhood system
JO - Applicationes Mathematicae
PY - 2001
VL - 28
IS - 2
SP - 169
EP - 180
AB - This paper deals with the properties of self-avoiding walks defined on the lattice with the 8-neighbourhood system. We compute the number of walks, bridges and mean-square displacement for N=1 through 13 (N is the number of steps of the self-avoiding walk). We also estimate the connective constant and critical exponents, and study finite memory and generating functions. We show applications of this kind of walk. In addition, we compute upper bounds for the number of walks and the connective constant.
LA - eng
KW - self-avoiding walk; lattice with the 8-neighbourhood system; connective constant; critical exponent; mean-square displacement
UR - http://eudml.org/doc/279713
ER -