{"paper":{"title":"Self-similar solutions of kinetic-type equations: the boundary case","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Alexander Marynych, Dariusz Buraczewski, Kamil Bogus","submitted_at":"2018-04-15T19:58:43Z","abstract_excerpt":"For a time dependent family of probability measures $(\\rho_t)_{t\\ge 0}$ we consider a kinetic-type evolution equation $\\partial \\phi_t/\\partial t + \\phi_t = \\widehat{Q} \\phi_t$ where $\\widehat{Q}$ is a smoothing transform and $\\phi_t$ is the Fourier--Stieltjes transform of $\\rho_t$. Assuming that the initial measure $\\rho_0$ belongs to the domain of attraction of a stable law, we describe asymptotic properties of $\\rho_t$, as $t\\to\\infty$. We consider the critical regime when the standard normalization leads to a degenerate limit and find an appropriate scaling ensuring a non-degenerate self-s"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.05418","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"}