Growth and roughness of the interface for ballistic deposition
| dc.creator | Penrose, Mathew D. | |
| dc.date | 2006-08-22 | |
| dc.date.accessioned | 2026-07-07T07:22:01Z | |
| dc.date.available | 2026-07-07T07:22:01Z | |
| dc.description | In ballistic deposition (BD), $(d+1)$-dimensional particles fall sequentially at random towards an initially flat, large but bounded $d$-dimensional surface, and each particle sticks to the first point of contact. For both lattice and continuum BD, a law of large numbers in the thermodynamic limit establishes convergence of the mean height and surface width of the interface to constants $h(t)$ and $w(t)$, respectively, depending on time $t$. We show that $h(t)$ is asymptotically linear in $t$, while $w(t)$ grows at least logarithmically in $t$ when $d=1$. We also give duality results saying that the height above the origin for deposition onto an initially flat surface is equidistributed with the maximum height for deposition onto a surface growing from a single site. | |
| dc.description | 26 pages. 1 figure | |
| dc.identifier | https://arxiv.org/abs/math/0608540 | |
| dc.identifier | http://arxiv.org/abs/math/0608540 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/115513 | |
| dc.subject | Probability | |
| dc.subject | Mathematical Physics | |
| dc.subject | 60K35 (Primary). 82C22, 60D05, 60E15 (Secondary) | |
| dc.title | Growth and roughness of the interface for ballistic deposition | |
| dc.type | text |