Abstract
We revisit the anchored Toom interface and use Kardar-Parisi-Zhang scaling theory to argue that the interface fluctuations are governed by the Airy1 process with the role of space and time interchanged. The predictions, which contain no free parameter, are numerically well confirmed for space-time statistics in the stationary state. In particular, the spatial fluctuations of the interface computed numerically agree well with those given by the GOE edge distribution of Tracy and Widom.
| Original language | English |
|---|---|
| Article number | 042116 |
| Number of pages | 8 |
| Journal | Physical Review. E, Statistical, nonlinear, and soft matter physics |
| Volume | 90 |
| Issue number | 4 |
| DOIs | |
| Publication status | Published - 8 Oct 2014 |
Funding
We thank Michael Prahofer, Jeremy Quastel, and Gene Speer for very helpful comments. The work was mostly done when the three last authors stayed at the Institute for Advanced Study, Princeton. We are grateful for the support. The work of J.L.L. was supported by NSF Grant No. DMR-1104501. P.L.F. was supported by the German Research Foundation via the SFB 1060-B04 project.
Keywords
- SIMPLE EXCLUSION PROCESS
- NONEQUILIBRIUM INTERFACE
- FLUCTUATIONS
- DIMENSIONS
- SYSTEMS
- GROWTH
- LIMIT
- MODEL