{"paper":{"title":"Heat kernels of non-symmetric jump processes: beyond the stable case","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Panki Kim, Renming Song, Zoran Vondra\\v{c}ek","submitted_at":"2016-06-07T02:39:20Z","abstract_excerpt":"Let $J$ be the L\\'evy density of a symmetric L\\'evy process in $\\mathbb{R}^d$ with its L\\'evy exponent satisfying a weak lower scaling condition at infinity. Consider the non-symmetric and non-local operator $$ {\\mathcal L}^{\\kappa}f(x):= \\lim_{\\epsilon \\downarrow 0} \\int_{\\{z \\in \\mathbb{R}^d: |z|>\\epsilon\\}}(f(x+z)-f(x))\\kappa(x,z)J(z)\\, dz\\, , $$ where $\\kappa(x,z)$ is a Borel measurable function on $\\mathbb{R}^d\\times \\mathbb{R}^d$ satisfying $0<\\kappa_0\\le \\kappa(x,z)\\le \\kappa_1$, $\\kappa(x,z)=\\kappa(x,-z)$ and $|\\kappa(x,z)-\\kappa(y,z)|\\le \\kappa_2|x-y|^{\\beta}$ for some $\\beta\\in (0, 1"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.02005","kind":"arxiv","version":3},"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"}