Résumé : In their recent paper proving the connective constant mu of self-avoiding walks (SAWs) on the hexagonal (honeycomb) lattice, Duminil-Copin and Smirnov consider the generating function of self-avoiding bridges which span a strip of width T, and conjecture that this generating function vanishes at 1/mu in the large T limit. This generating function was again considered by Bousquet-Mélou, de Gier, Duminil-Copin, Guttmann and myself when we studied the adsorption of SAWs onto an impenetrable surface, and we proved the conjecture of Duminil-Copin and Smirnov. I will discuss this conjecture and its proof, as well as what happens after rotating the lattice by pi/4. http://arxiv.org/abs/1109.0358 http://arxiv.org/abs/1210.0274

Dernière modification : Thursday 21 November 2024

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