{"paper":{"title":"Trace estimates for relativistic stable processes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Hyunchul Park, Renming Song","submitted_at":"2012-12-12T19:51:17Z","abstract_excerpt":"In this paper, we study the asymptotic behavior, as the time $t$ goes to zero, of the trace of the semigroup of a killed relativistic $\\alpha$-stable process in bounded $C^{1,1}$ open sets and bounded Lipschitz open sets. More precisely, we establish the asymptotic expansion in terms of $t$ of the trace with an error bound of order $t^{2/\\alpha}t^{-d/\\alpha}$ for $C^{1,1}$ open sets and of order $t^{1/\\alpha}t^{-d/\\alpha}$ for Lipschitz open sets. Compared with the corresponding expansions for stable processes, there are more terms between the orders $t^{-d/\\alpha}$ and $t^{(2-d)/\\alpha}$ for "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.2943","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"}