Open Access
2017 Scaling limit of the uniform prudent walk
Nicolas Pétrélis, Rongfeng Sun, Niccolò Torri
Electron. J. Probab. 22: 1-19 (2017). DOI: 10.1214/17-EJP87


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 [3], while another variant, the kinetic prudent walk has been analyzed in detail in [2]. 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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Nicolas Pétrélis. Rongfeng Sun. Niccolò Torri. "Scaling limit of the uniform prudent walk." Electron. J. Probab. 22 1 - 19, 2017.


Received: 21 February 2017; Accepted: 26 July 2017; Published: 2017
First available in Project Euclid: 7 September 2017

zbMATH: 1377.82028
MathSciNet: MR3698735
Digital Object Identifier: 10.1214/17-EJP87

Primary: 82B41
Secondary: 60F05 , 60K35

Keywords: prudent walk , scaling limits , Self-avoiding walk

Vol.22 • 2017
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