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Pré-Publication, Document De Travail Année : 2017

Scaling limit of the uniform prudent walk

Résumé

We study the 2-dimensional uniform prudent self-avoiding walk, which assigns equal probability to all nearest-neighbor self-avoiding paths of a fixed length that respect the prudent condition, namely, the path cannot take any step in the direction of a previously visited site. The uniform prudent walk has been investigated with combinatorial techniques in [Bousquet-Mélou, 2010], while another variant, the kinetic prudent walk has been analyzed in detail in [Beffara, Friedli and Velenik, 2010]. In this paper, we prove that the 2-dimensional uniform prudent walk is ballistic and follows one of the 4 diagonals with equal probability. We also establish a functional central limit theorem for the fluctuations of the path around the diagonal.
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Dates et versions

hal-01470125 , version 1 (17-02-2017)
hal-01470125 , version 2 (07-09-2017)

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Nicolas Pétrélis, Rongfeng Sun, Niccolò Torri. Scaling limit of the uniform prudent walk. 2017. ⟨hal-01470125v1⟩
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