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

doi:10.1007/s10473-023-0209-1

Acta mathematica scientia,Series B ›› 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 Li^2,†

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).

Abstract

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

Yangyang Lyu, Heyu Li. ALMOST SURELY TIME-SPACE INTERMITTENCY FOR THE PARABOLIC ANDERSON MODEL WITH A LOG-CORRELATED GAUSSIAN FIELD^*[J].Acta mathematica scientia,Series B, 2023, 43(2): 608-639.

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

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