{"paper":{"title":"On the regularity of complex multiplicative chaos","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Eero Saksman, Janne Junnila, Lauri Viitasaari","submitted_at":"2019-05-28T18:46:54Z","abstract_excerpt":"Denote by $\\mu_\\beta=\"\\exp(\\beta X)\"$ the Gaussian multiplicative chaos which is defined using a log-correlated Gaussian field $X$ on a domain $U\\subset\\mathbb{R}^d$. The case $\\beta\\in\\mathbb{R}$ has been studied quite intensively, and then $\\mu_\\beta$ is a random measure on $U$. It is known that $\\mu_\\beta$ can also be defined for complex values $\\beta$ lying in certain subdomain of $\\mathbb{C}$, and then the realizations of $\\mu_\\beta$ are random generalized functions on $U$. In this note we complement the results of Junnila et al. (where the case of purely imaginary $\\beta$ was considered)"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.12027","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"}