ALMOST SURELY TIME-SPACE INTERMITTENCY FOR THE PARABOLIC ANDERSON MODEL WITH A LOG-CORRELATED GAUSSIAN FIELD&#x0002A;

Yangyang Lyu; Heyu Li

doi:10.1007/s10473-023-0209-1

Acta mathematica scientia, Series B >

2023 , Vol. 43 >Issue 2: 608 - 639

DOI: https://doi.org/10.1007/s10473-023-0209-1

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

Yangyang Lyu ,
Heyu Li

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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

Yangyang Lyu, E-mail: yijiaobingshan@126.com

Received date: 2021-09-30

Revised date: 2022-01-18

Online published: 2023-04-12

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).

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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

Cite this article

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 . DOI: 10.1007/s10473-023-0209-1

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