{"paper":{"title":"Hausdorff and packing spectra, large deviations, and free energy for branching random walks in $\\R^d$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MG","math.MP","math.PR"],"primary_cat":"math-ph","authors_text":"Julien Barral, Najmeddine Attia","submitted_at":"2013-05-09T08:52:02Z","abstract_excerpt":"Consider an $\\R^d$-valued branching random walk (BRW) on a supercritical Galton Watson tree. Without any assumption on the distribution of this BRW we compute, almost surely and simultaneously, the Hausdorff and packing dimensions of the level sets $E(K)$ of infinite branches in the boundary of the tree (endowed with its standard metric) along which the averages of the BRW have a given closed connected set of limit points $K$. This goes beyond multifractal analysis, which only considers those level sets when $K$ ranges in the set of singletons $\\{\\alpha\\}$, $\\alpha\\in\\R^d$. We also give a $0$-"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.2034","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"}