2010/06/30 by Konstantin Khanin, Sergei Nechaev, Gleb Oshanin +2 · 1 citation
Physics and Astronomy · #cond-mat.stat-mech
paper · pdf · doi:10.1103/physreve.82.061107
published as Phys. Rev. E 82, 061107 (2010) · 10 pages, 5 figures. Minor edits: typo corrected, added explanation of two acronyms. The text is essentially equivalent to version 1
arxiv created 2010/07/16 · arxiv updated 2011/03/09
We consider a (1+1)-dimensional ballistic deposition process with next-nearest neighbor interaction, which belongs to the KPZ universality class, and introduce for this discrete model a variational formulation similar to that for the randomly forced continuous Burgers equation. This allows to identify the characteristic structures in the bulk of a growing aggregate ("clusters" and "crevices") with minimizers and shocks in the Burgers turbulence, and to introduce a new kind of equipped Airy process for ballistic growth. We dub it the "hairy Airy process" and investigate its statistics numerically. We also identify scaling laws that characterize the ballistic deposition patterns in the bulk: the law of "thinning" of the forest of clusters with increasing height, the law of transversal fluctuations of cluster boundaries, and the size distribution of clusters. The corresponding critical exponents are determined exactly based on the analogy with the Burgers turbulence and simple scaling considerations.