What is the difference between a square and a triangle?
Probability
2008-05-20 v2
Abstract
We offer a reader-friendly introduction to the attracting edge problem (also known as the "triangle conjecture") and its most general current solution of Limic and Tarr\`es (2007). Little original research is reported; rather this article ``zooms in'' to describe the essential characteristics of two different techniques/approaches verifying the almost sure existence of the attracting edge for the strongly edge reinforced random walk (SERRW) on a square. Both arguments extend straightforwardly to the SERRW on even cycles. Finally, we show that the case where the underlying graph is a triangle cannot be studied by a simple modification of either of the two techniques.
Keywords
Cite
@article{arxiv.0712.0958,
title = {What is the difference between a square and a triangle?},
author = {V. Limic and P. Tarres},
journal= {arXiv preprint arXiv:0712.0958},
year = {2008}
}
Comments
18 pages, 1 figure