数学物理学报(英文版) ›› 2023, Vol. 43 ›› Issue (2): 608-639.doi: 10.1007/s10473-023-0209-1

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ALMOST SURELY TIME-SPACE INTERMITTENCY FOR THE PARABOLIC ANDERSON MODEL WITH A LOG-CORRELATED GAUSSIAN FIELD*

Yangyang Lyu1, Heyu Li2,†   

  1. 1. School of Mathematics and Statistics, Minnan Normal University, Zhangzhou 363000, China;
    2. School of Mathematics and Statistics, Changchun University of Technology, Changchun 130012, China
  • 收稿日期:2021-09-30 修回日期:2022-01-18 出版日期:2023-03-25 发布日期:2023-04-12
  • 通讯作者: †Heyu Li, E-mail: liheyu@ccut.edu.cn.
  • 作者简介:Yangyang Lyu, E-mail: yijiaobingshan@126.com
  • 基金资助:
    The first author was supported by the National Natural Science Foundation of China (12201282), the Institute of Meteorological Big Data-Digital Fujian and the Fujian Key Laboratory of Data Science and Statistics (2020L0705) and the Education Department of Fujian Province (JAT200325).

ALMOST SURELY TIME-SPACE INTERMITTENCY FOR THE PARABOLIC ANDERSON MODEL WITH A LOG-CORRELATED GAUSSIAN FIELD*

Yangyang Lyu1, Heyu Li2,†   

  1. 1. School of Mathematics and Statistics, Minnan Normal University, Zhangzhou 363000, China;
    2. School of Mathematics and Statistics, Changchun University of Technology, Changchun 130012, China
  • Received:2021-09-30 Revised:2022-01-18 Online:2023-03-25 Published:2023-04-12
  • Contact: †Heyu Li, E-mail: liheyu@ccut.edu.cn.
  • About author:Yangyang Lyu, E-mail: yijiaobingshan@126.com
  • Supported by:
    The first author was supported by the National Natural Science Foundation of China (12201282), the Institute of Meteorological Big Data-Digital Fujian and the Fujian Key Laboratory of Data Science and Statistics (2020L0705) and the Education Department of Fujian Province (JAT200325).

摘要: In this paper, we consider the continuous parabolic Anderson model with a log-correlated Gaussian field, and obtain the precise quenched long-time asymptotics and spatial asymptotics. To overcome the difficulties arising from the log-correlated Gaussian field in the proof of the lower bound of the spatial asymptotics, we first establish the relation between quenched long-time asymptotics and spatial asymptotics, and then get the lower bound of the spatial asymptotics through the lower bound of the quenched long-time asymptotics.

关键词: spatial asymptotics, quenched long-time asymptotics, parabolic Anderson model, log-correlated Gaussian field, Feynman-Kac formula

Abstract: In this paper, we consider the continuous parabolic Anderson model with a log-correlated Gaussian field, and obtain the precise quenched long-time asymptotics and spatial asymptotics. To overcome the difficulties arising from the log-correlated Gaussian field in the proof of the lower bound of the spatial asymptotics, we first establish the relation between quenched long-time asymptotics and spatial asymptotics, and then get the lower bound of the spatial asymptotics through the lower bound of the quenched long-time asymptotics.

Key words: spatial asymptotics, quenched long-time asymptotics, parabolic Anderson model, log-correlated Gaussian field, Feynman-Kac formula