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Scaling Limit of the Prudent Walk
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Vincent Beffara, UMPA
Sacha Friedli, UFMG
Yvan Velenik, Université de Genève
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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 σ1,σ2 two random signs. In particular, the asymptotic speed of the walk is well-defined in the L1-norm and equals 3/7.
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Full text: PDF
Pages: 44-58
Published on: February 24, 2010
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Electronic Communications in Probability. ISSN: 1083-589X |
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