English

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

R2 v1 2026-06-21T09:51:15.605Z