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 Electronic Communications in Probability > Vol. 15(2010) > Paper 5 open journal systems 


Scaling Limit of the Prudent Walk

Vincent Beffara, UMPA
Sacha Friedli, UFMG
Yvan Velenik, Université de Genève


Abstract
We describe the scaling limit of the nearest neighbour prudent walk on Z2, 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 $Z_u = int_0^{3u/7} ( σ11W(s)≥ 0 vec{e}1 + σ21W(s)< 0 vec{e}2 ) ds$, u ∈ [0,1], where W is the one-dimensional Brownian motion and σ12 two random signs. In particular, the asymptotic speed of the walk is well-defined in the L1-norm and equals 3/7.


Full text: PDF

Pages: 44-58

Published on: February 24, 2010


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Electronic Communications in Probability. ISSN: 1083-589X