@inproceedings{UMPA2010ScalingLO,
title={Scaling Limit of the Prudent Walk},
author={UMPA and All{\'e}e d’Italie},
year={2010}
}

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 .

and as yet unsolvable, polygon and walk models. International Workshop on Statistical Mechanics and Combinatorics: Counting Complexity, 42:98– 110 • 2006

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Some solvable , and as yet unsolvable , polygon and walk models

P. Major J. Komlós, G. Tusnády

Inter - national Workshop on Statistical Mechanics and Combinatorics : Counting Complexity • 2006