@article{da7a5c54bf8d4995a479593bbb543289,
title = "Translation-invariant probability measures on entire functions",
abstract = "We study non-trivial translation-invariant probability measures on the space of entire functions of one complex variable. The existence (and even an abundance) of such measures was proven by Benjamin Weiss. Answering Weiss{\textquoteright} question, we find a relatively sharp lower bound for the growth of entire functions in the support of such measures. The proof of this result consists of two independent parts: the proof of the lower bound and the construction, which yields its sharpness. Each of these parts combines various tools (both classical and new) from the theory of entire and subharmonic functions and from the ergodic theory. We also prove several companion results, which concern the decay of the tails of non-trivial translation-invariant probability measures on the space of entire functions and the growth of locally uniformly recurrent entire and meromorphic functions.",
author = "Lev Buhovsky and Adi Gl{\"u}cksam and Alexander Logunov and Mikhail Sodin",
note = "Funding Information: We study non-trivial translation-invariant probability measures on the space of entire functions of one complex variable. The existence (and even an abundance) of such measures was proven by Benjamin Weiss. Answering Weiss{\textquoteright} question, we find a relatively sharp lower bound for the growth of entire functions in the support of such measures. The proof of this result consists of two independent parts: the proof of the lower bound and the construction, which yields its sharpness. Each of these parts combines various tools (both classical and new) from the theory of entire and subharmonic functions and from the ergodic theory. We also prove several companion results, which concern the decay of the tails of non-trivial translation-invariant probability measures on the space of entire functions and the growth of locally uniformly recurrent entire and meromorphic functions. publisher-imprint-name Hebrew University Magnes Press article-contains-esm No article-numbering-style Unnumbered article-registration-date-year 2019 article-registration-date-month 10 article-registration-date-day 29 article-toc-levels 0 journal-product ArchiveJournal numbering-style Unnumbered article-grants-type Regular metadata-grant OpenAccess abstract-grant OpenAccess bodypdf-grant Restricted bodyhtml-grant Restricted bibliography-grant Restricted esm-grant OpenAccess online-first true pdf-file-reference BodyRef/PDF/11854_2019_Article_67.pdf target-type OnlinePDF article-type OriginalPaper journal-subject-primary Mathematics journal-subject-secondary Analysis journal-subject-secondary Functional Analysis journal-subject-secondary Dynamical Systems and Ergodic Theory journal-subject-secondary Abstract Harmonic Analysis journal-subject-secondary Partial Differential Equations journal-subject-collection Mathematics and Statistics open-access false Supported in part by ISF Grant 1380/13, and by the Alon Fellowship. Supported in part by ERC Advanced Grant 692616 and ISF Grant 382/15. Supported in part by ERC Advanced Grant 692616 and ISF Grants 1380/13, 382/15. Supported in part by ERC Advanced Grant 692616 and ISF Grant 382/15. Publisher Copyright: {\textcopyright} 2019, The Hebrew University of Jerusalem.",
year = "2019",
month = oct,
day = "1",
doi = "10.1007/s11854-019-0067-x",
language = "English (US)",
volume = "139",
pages = "307--339",
journal = "Journal d'Analyse Mathematique",
issn = "0021-7670",
publisher = "Springer New York",
number = "1",
}