{"paper":{"title":"Regularity and irregularity of superprocesses with $(1+\\beta)$-stable branching mechanism","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Leonid Mytnik, Vitali Wachtel","submitted_at":"2015-08-09T20:36:31Z","abstract_excerpt":"We would like to give an overview of results on regularity, or better to say \"irregularity\", properties of densities at fixed times of super-Brownian motion with $(1+\\beta)$-stable branching for $\\beta<1$. First, the following dichotomy for the density is shown: it is continuous in the dimension $d=1$ and locally unbounded in all higher dimensions where it exists. Then in $d=1$ we determine pointwise and local H\\\"older exponents of the density, and calculate the multifractal spectrum corresponding to pointwise H\\\"older exponents."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.02081","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"}