Random ballistic growth and diffusion in symmetric spaces
Abstract
Sequential ballistic deposition (BD) with next-nearest-neighbor (NNN) interactions in a N-column box is viewed a time-ordered product of N\times N-matrices consisting of a single sl_2-block which has a random position along the diagonal. We relate the uniform BD growth with the diffusion in the symmetric space H_N=SL(N,R)/SO(N). In particular, the distribution of the maximal height of a growing heap is connected with the distribution of the maximal distance for the diffusion process in H_N. The coordinates of H_N are interpreted as the coordinates of particles of the one--dimensional Toda chain. The group-theoretic structure of the system and links to some random matrix models are also discussed.
Keywords
Cite
@article{arxiv.1110.3524,
title = {Random ballistic growth and diffusion in symmetric spaces},
author = {A. Gorsky and S. Nechaev and R. Santachiara and G. Schehr},
journal= {arXiv preprint arXiv:1110.3524},
year = {2012}
}
Comments
29 pages, 7 figures. Revised and published version. To appear in Nuclear Physics B