منابع مشابه
Self-Avoiding Walks and Amenability
The connective constant μ(G) of an infinite transitive graph G is the exponential growth rate of the number of self-avoiding walks from a given origin. The relationship between connective constants and amenability is explored in the current work. Various properties of connective constants depend on the existence of so-called ‘unimodular graph height functions’, namely: (i) whether μ(G) is a loc...
متن کاملAnisotropic Self - Avoiding Walks
We consider a model of self-avoiding walks on the lattice Zd with different weights for steps in each of the 2d lattice directions. We find that the directiondependent mass for the two-point function of this model has three phases: mass positive in all directions; mass identically −∞; and masses of different signs in different directions. The final possibility can only occur if the weights are ...
متن کاملPrudent Self-Avoiding Walks
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.
متن کاملExtendable Self-avoiding Walks
The connective constant μ of a graph is the exponential growth rate of the number of n-step self-avoiding walks starting at a given vertex. A self-avoiding walk is said to be forward (respectively, backward) extendable if it may be extended forwards (respectively, backwards) to a singly infinite self-avoiding walk. It is called doubly extendable if it may be extended in both directions simultan...
متن کاملCounting Self-avoiding Walks
The connective constant μ(G) of a graph G is the asymptotic growth rate of the number of self-avoiding walks on G from a given starting vertex. We survey three aspects of the dependence of the connective constant on the underlying graph G. Firstly, when G is cubic, we study the effect on μ(G) of the Fisher transformation (that is, the replacement of vertices by triangles). Secondly, we discuss ...
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ژورنال
عنوان ژورنال: The Electronic Journal of Combinatorics
سال: 2017
ISSN: 1077-8926
DOI: 10.37236/6577