{"paper":{"title":"Heat kernel estimates for Markov processes with blowing-up jump kernels","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.PR","authors_text":"Panki Kim, Renming Song, Soobin Cho, Zoran Vondra\\v{c}ek","submitted_at":"2025-12-31T11:49:51Z","abstract_excerpt":"In this paper, we establish sharp two-sided heat kernel estimates for a large class of purely discontinuous symmetric Markov processes on closed subsets $F$ of $\\mathbb{R}^d$, whose jump kernels blow up on a Borel subset $\\Sigma$ of $F$. We assume that $F\\setminus \\Sigma$ is a $\\kappa$-fat set and is dense in $F$. To the best of our knowledge, this is the first work establishing sharp heat kernel estimates for jump processes whose jump kernels blow up on part of the state space.\n  The jump kernels under consideration take the form $J(x,y)=|x-y|^{-d-\\alpha}{\\mathcal B}(x,y)$, where $\\alpha\\in ("},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2512.24807","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2512.24807/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}