Scaling Limit of the Prudent Walk
| Dublin Core | PKP Metadata Items | Metadata for this Document | |
| 1. | Title | Title of document | Scaling Limit of the Prudent Walk |
| 2. | Creator | Author's name, affiliation, country | Vincent Beffara; UMPA |
| 2. | Creator | Author's name, affiliation, country | Sacha Friedli; UFMG |
| 2. | Creator | Author's name, affiliation, country | Yvan Velenik; Université de Genève |
| 3. | Subject | Discipline(s) | |
| 3. | Subject | Keyword(s) | prudent self-avoiding walk, brownian motion, scaling limit, ballistic behaviour, ageing |
| 3. | Subject | Subject classification | 60F17; 60G50; 60G52 |
| 4. | Description | Abstract | 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. |
| 5. | Publisher | Organizing agency, location | |
| 6. | Contributor | Sponsor(s) | CNPq, Fonds National Suisse |
| 7. | Date | (YYYY-MM-DD) | 2010-02-24 |
| 8. | Type | Status & genre | Peer-reviewed Article |
| 8. | Type | Type | |
| 9. | Format | File format | |
| 10. | Identifier | Uniform Resource Identifier | http://ecp.ejpecp.org/article/view/1527 |
| 10. | Identifier | Digital Object Identifier | 10.1214/ECP.v15-1527 |
| 11. | Source | Journal/conference title; vol., no. (year) | Electronic Communications in Probability; Vol 15 |
| 12. | Language | English=en | |
| 14. | Coverage | Geo-spatial location, chronological period, research sample (gender, age, etc.) | |
| 15. | Rights | Copyright and permissions | The Electronic Journal of Probability applies the Creative Commons Attribution License (CCAL) to all articles we publish in this journal. Under the CCAL, authors retain ownership of the copyright for their article, but authors allow anyone to download, reuse, reprint, modify, distribute, and/or copy articles published in EJP, so long as the original authors and source are credited. This broad license was developed to facilitate open access to, and free use of, original works of all types. Applying this standard license to your work will ensure your right to make your work freely and openly available. Summary of the Creative Commons Attribution License You are free
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