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 σ1,σ2 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
Copyright for articles published in this journal is retained by the authors, with first publication rights granted to the journal. By virtue of their appearance in this open access journal, articles are free to use, with proper attribution, in educational and other non-commercial settings.
The authors of papers published in EJP/ECP retain the copyright. We ask for the permission to use the material in any form. We also require that the initial publication in EJP or ECP is acknowledged in any future publication of the same article.
Before a paper is published in the Electronic Journal of Probability or Electronic Communications in Probability we must receive a hard-copy of the copyright form. Please mail it to
Philippe Carmona
Laboratoire Jean Leray UMR 6629
Universite de Nantes,
2, Rue de la Houssinière BP 92208
F-44322 Nantes Cédex 03
France
You can also send it by FAX: (33|0) 2 51 12 59 12 to the attention of Philippe Carmona.
The preferred way is to send a scanned (jpeg or pdf) copy of the signed copyright form to the managing editor Philippe Carmona at ejpecpme@math.univ-nantes.fr.
If a paper has several authors, the corresponding author signs the copyright form
on behalf of all the authors.