| Título: | Scaling Limit of the Prudent Walk |
| Autores: |
Beffara, Vincent; UMPA Friedli, Sacha; UFMG Velenik, Yvan; Université de Genève |
| Fecha: | 2010-01-01 |
| Publicador: | Electronic communications in probability |
| Fuente: |
 |
| Tipo: |
Peer-reviewed Article |
| Tema: |
prudent self-avoiding walk, brownian motion, scaling limit, ballistic behaviour, ageing 60F17; 60G50; 60G52 |
| Descripción: | We describe the scaling limit of the nearest neighbour prudent walk on $Z^2$, 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 $Z_u = \int_0^{3u/7} ( \sigma_1 1_{W(s)\geq 0}\vec{e}_1 + \sigma_2 1_{W(s)\geq 0}\vec{e}_2 ) ds$, $u \in [0,1]$, where $W$ is the one-dimensional Brownian motion and $\sigma_1, \sigma_2$ two random signs. In particular, the asymptotic speed of the walk is well-defined in the $L^1$-norm and equals 3/7. |
| Idioma: | No aplica |
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