{"paper":{"title":"An explicit effect of non-symmetry of random walks on the triangular lattice","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Hiroshi Kawabi, Satoshi Ishiwata, Tsubasa Teruya","submitted_at":"2012-10-30T13:01:38Z","abstract_excerpt":"In the present paper, we study an explicit effect of non-symmetry on asymptotics of the $n$-step transition probability as $n\\rightarrow \\infty$ for a class of non-symmetric random walks on the triangular lattice. Realizing the triangular lattice into $\\mathbb{R}^2$ appropriately, we observe that the Euclidean distance in $\\mathbb{R}^2$ naturally appears in the asymptotics. We characterize this realization from a geometric view point of Kotani-Sunada's standard realization of crystal lattices. As a corollary of the main theorem, we prove that the transition semigroup generated by the non-symme"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.7989","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"}