{"paper":{"title":"Hydrodynamic limit and viscosity solutions for a 2D growth process in the anisotropic KPZ class","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Fabio Lucio Toninelli (CNRS, Lyon 1), Martin Legras (Lyon 1)","submitted_at":"2017-04-21T14:54:15Z","abstract_excerpt":"We study a $(2+1)$-dimensional stochastic interface growth model, that is believed to belong to the so-called Anisotropic KPZ (AKPZ) universality class [Borodin and Ferrari, 2014]. It can be seen either as a two-dimensional interacting particle process with drift, that generalizes the one-dimensional Hammersley process [Aldous and Diaconis 1995, Seppalainen 1996], or as an irreversible dynamics of lozenge tilings of the plane [Borodin and Ferrari 2014, Toninelli 2015]. Our main result is a hydrodynamic limit: the interface height profile converges, after a hyperbolic scaling of space and time,"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.06581","kind":"arxiv","version":1},"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"}