{"paper":{"title":"Random ballistic growth and diffusion in symmetric spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech","math.MP","math.PR"],"primary_cat":"math-ph","authors_text":"A. Gorsky, G. Schehr, R. Santachiara, S. Nechaev","submitted_at":"2011-10-16T20:53:47Z","abstract_excerpt":"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 chai"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.3524","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}