First-exit-time probability density tails for a local height of a non-equilibrium Gaussian interface
| dc.creator | Oshanin, G. | |
| dc.date | 2008-01-25 | |
| dc.date.accessioned | 2026-07-07T08:56:31Z | |
| dc.date.available | 2026-07-07T08:56:31Z | |
| dc.description | We study the long-time behavior of the probability density Q_t of the first exit time from a bounded interval [-L,L] for a stochastic non-Markovian process h(t) describing fluctuations at a given point of a two-dimensional, infinite in both directions Gaussian interface. We show that Q_t decays when t \to \infty as a power-law $^{-1 - α}, where αis non-universal and proportional to the ratio of the thermal energy and the elastic energy of a fluctuation of size L. The fact that αappears to be dependent on L, which is rather unusual, implies that the number of existing moments of Q_t depends on the size of the window [-L,L]. A moment of an arbitrary order n, as a function of L, exists for sufficiently small L, diverges when L approaches a certain threshold value L_n, and does not exist for L > L_n. For L > L_1, the probability density Q_t is normalizable but does not have moments. | |
| dc.description | 10 pages | |
| dc.identifier | https://arxiv.org/abs/0801.3975 | |
| dc.identifier | http://arxiv.org/abs/0801.3975 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/146637 | |
| dc.subject | Statistical Mechanics | |
| dc.subject | Probability | |
| dc.title | First-exit-time probability density tails for a local height of a non-equilibrium Gaussian interface | |
| dc.type | text |