What is the difference between a square and a triangle?

V. Limic; P. Tarres

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arXiv · 0712.0958

What is the difference between a square and a triangle?

V. Limic·P. Tarres

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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 Tarrès (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.

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V. Limic, P. Tarres. 2008-05-20. What is the difference between a square and a triangle?. https://arxiv.org/abs/0712.0958

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