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## Abstract

Let (Formula Presented) be an entire function on the complex plane, and let (Formula Presented) be its randomization induced by a standard sequence of independent Bernoulli, Steinhaus, or Gaussian random variables. In this paper, we characterize those functions such that is almost surely in the Fock space for any. Then such a characterization, together with embedding theorems which are of independent interests, is used to obtain a Littlewood-type theorem, also known as regularity improvement under randomization within the scale of Fock spaces. Other results obtained in this paper include: (a) a characterization of random analytic functions in the mixed-norm space, an endpoint version of Fock spaces, via entropy integrals; (b) a complete description of random lacunary elements in Fock spaces; and (c) a complete description of random multipliers between different Fock spaces.

Original language | English |
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Pages (from-to) | 1176-1198 |

Number of pages | 23 |

Journal | Canadian Journal of Mathematics |

Volume | 75 |

Issue number | 4 |

DOIs | |

State | Published - 8 Aug 2023 |

## Keywords

- Fock spaces
- Random analytic functions
- mixed norm space

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Dive into the research topics of 'Two problems on random analytic functions in Fock spaces'. Together they form a unique fingerprint.## Projects

- 1 Finished