{"paper":{"title":"Self-similar stable processes arising from high-density limits of occupation times of particle systems","license":"","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Anna Talarczyk, Luis G. Gorostiza, Tomasz Bojdecki","submitted_at":"2007-09-06T04:38:51Z","abstract_excerpt":"We extend results on time-rescaled occupation time fluctuation limits of the $(d,\\alpha, \\beta)$-branching particle system $(0<\\alpha \\leq 2, 0<\\beta \\leq 1)$ with Poisson initial condition. The earlier results in the homogeneous case (i.e., with Lebesgue initial intensity measure) were obtained for dimensions $d>\\alpha / \\beta$ only, since the particle system becomes locally extinct if $d\\le \\alpha / \\beta$. In this paper we show that by introducing high density of the initial Poisson configuration, limits are obtained for all dimensions, and they coincide with the previous ones if $d>\\alpha/"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0709.0773","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"}