High-dimensional graphical networks of self-avoiding walks
نویسندگان
چکیده
We use the lace expansion to analyse networks of mutually-avoiding self-avoiding walks, having the topology of a graph. The networks are defined in terms of spread-out self-avoiding walks that are permitted to take large steps. We study the asymptotic behaviour of networks in the limit of widely separated network branch points, and prove Gaussian behaviour for sufficiently spread-out networks on Zd in dimensions d > 4. Subject classifications: Primary 82B41, Secondary 60K35.
منابع مشابه
The lace expansion on a tree with application to networks of self-avoiding walks
The lace expansion has been used successfully to study the critical behaviour in high dimensions of self-avoiding walks, lattice trees and lattice animals, and percolation. In each case, the lace expansion has been an expansion along a time interval. In this paper, we introduce the lace expansion on a tree, in which ‘time’ is generalised from an interval to a tree. We develop the expansion in t...
متن کاملUnbinding of mutually avoiding random walks and two-dimensional quantum gravity.
We analyze the unbinding transition for a two-dimensional lattice polymer in which the constituent strands are mutually avoiding random walks. At low temperatures the strands are bound and form a single self-avoiding walk. We show that unbinding in this model is a strong first order transition. The entropic exponents associated with denaturated loops and end-segment distributions show sharp dif...
متن کاملBallistic behavior for biased self-avoiding walks
For self-avoiding walks on the d-dimensional cubic lattice defined with a positive bias in one of the coordinate directions, it is proved that the drift in the favored direction is strictly positive. c © 2008 Elsevier B.V. All rights reserved. Keyword: Biased self-avoiding walks
متن کاملCorrection-to-Scaling Exponents for Two-Dimensional Self-Avoiding Walks
We study the correction-to-scaling exponents for the two-dimensional selfavoiding walk, using a combination of series-extrapolation and Monte Carlo methods. We enumerate all self-avoiding walks up to 59 steps on the square lattice, and up to 40 steps on the triangular lattice, measuring the mean-square end-to-end distance, the mean-square radius of gyration and the mean-square distance of a mon...
متن کاملPolygons and the Lace Expansion
We give an introduction to the lace expansion for self-avoiding walks, with emphasis on self-avoiding polygons, and with a focus on combinatorial rather than analytical aspects. We derive the lace expansion for self-avoiding walks, and show that this is equivalent to taking the reciprocal of the self-avoiding walk generating function. We list some of the rigorous results for self-avoiding walks...
متن کامل