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

作　　者：吕阳阳 李贺宇 Yangyang LYU;Heyu LI(School of Mathematics and Statistics,Minnan Normal University,Zhangzhou 363000,China;School of Mathematics and Statistics,Changchun University of Technology,Changchun 130012,China)

机构地区：[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

出　　处：《Acta Mathematica Scientia》2023年第2期608-639,共32页数学物理学报（B辑英文版）

基　　金：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);the Education Department of Fujian Province (JAT200325)。

摘　　要：In this paper, we consider the continuous parabolic Anderson model with a logcorrelated 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 

分 类 号：O175.26[理学—数学]