@article{ECP1527,
author = {Vincent Beffara and Sacha Friedli and Yvan Velenik},
title = {Scaling Limit of the Prudent Walk},
journal = {Electron. Commun. Probab.},
fjournal = {Electronic Communications in Probability},
volume = {15},
year = {2010},
keywords = {prudent self-avoiding walk, brownian motion, scaling limit, ballistic behaviour, ageing},
abstract = {We describe the scaling limit of the nearest neighbour prudent walk on $Z^2$, which performs steps uniformly in directions in which it does not see sites already visited. We show that the scaling limit is given by the process $Z_u = \int_0^{3u/7} ( \sigma_1 1_{W(s)\geq 0}\vec{e}_1 + \sigma_2 1_{W(s)\geq 0}\vec{e}_2 ) ds$, $u \in [0,1]$, where $W$ is the one-dimensional Brownian motion and $\sigma_1, \sigma_2$ two random signs. In particular, the asymptotic speed of the walk is well-defined in the $L^1$-norm and equals 3/7.},
pages = {no. 5, 44-58},
issn = {1083-589X},
doi = {10.1214/ECP.v15-1527},
url = {http://ecp.ejpecp.org/article/view/1527}}