Scaling Limit of the Prudent Walk

  title={Scaling Limit of the Prudent Walk},
  author={UMPA and All{\'e}e d’Italie},
  • UMPA, Allée d’Italie
  • Published 2010
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 Zu = ∫ 3u/7 0 σ11{W (s)≥0}~e1 +σ21{W (s)<0}~e2 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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