The random average process and random walk in a space-time random environment in one dimension
| dc.creator | Balazs, Marton | |
| dc.creator | Rassoul-Agha, Firas | |
| dc.creator | Seppalainen, Timo | |
| dc.date | 2005-07-11 | |
| dc.date | 2006-04-07 | |
| dc.date.accessioned | 2026-07-07T08:28:51Z | |
| dc.date.available | 2026-07-07T08:28:51Z | |
| dc.description | We study space-time fluctuations around a characteristic line for a one-dimensional interacting system known as the random average process. The state of this system is a real-valued function on the integers. New values of the function are created by averaging previous values with random weights. The fluctuations analyzed occur on the scale n^{1/4} where n is the ratio of macroscopic and microscopic scales in the system. The limits of the fluctuations are described by a family of Gaussian processes. In cases of known product-form equilibria, this limit is a two-parameter process whose time marginals are fractional Brownian motions with Hurst parameter 1/4. Along the way we study the limits of quenched mean processes for a random walk in a space-time random environment. These limits also happen at scale n^{1/4} and are described by certain Gaussian processes that we identify. In particular, when we look at a backward quenched mean process, the limit process is the solution of a stochastic heat equation. | |
| dc.description | 51 pages | |
| dc.identifier | https://arxiv.org/abs/math/0507226 | |
| dc.identifier | http://arxiv.org/abs/math/0507226 | |
| dc.identifier | Comm. Math. Phys. 266 (2006) 499-545 | |
| dc.identifier | doi:10.1007/s00220-006-0036-y | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/137768 | |
| dc.subject | Probability | |
| dc.subject | 60K35; 60K37; 60F05 | |
| dc.title | The random average process and random walk in a space-time random environment in one dimension | |
| dc.type | text |