Spatial ergodicity and central limit theorems for parabolic Anderson model with delta initial condition
| Autor: | Davar Khoshnevisan, Fei Pu, Le Chen, David Nualart |
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| Rok vydání: | 2020 |
| Předmět: |
Random field
010102 general mathematics Ergodicity Probability (math.PR) Order (ring theory) 01 natural sciences Combinatorics 010104 statistics & probability FOS: Mathematics Ergodic theory Initial value problem 0101 mathematics Anderson impurity model Analysis Heat kernel Mathematics - Probability Mathematics Central limit theorem |
| DOI: | 10.48550/arxiv.2005.10417 |
| Popis: | Let $\{u(t\,, x)\}_{t >0, x \in\mathbb{R}}$ denote the solution to the parabolic Anderson model with initial condition $\delta_0$ and driven by space-time white noise on $\mathbb{R}_+\times\mathbb{R}$, and let $p_t(x):= (2\pi t)^{-1/2}\exp\{-x^2/(2t)\}$ denote the standard Gaussian heat kernel on the line. We use a non-trivial adaptation of the methods in our companion papers \cite{CKNP,CKNP_b} in order to prove that the random field $x\mapsto u(t\,,x)/p_t(x)$ is ergodic for every $t >0$. And we establish an associated quantitative central limit theorem following the approach based on the Malliavin-Stein method introduced in Huang, Nualart, and Viitasaari \cite{HNV2018}. Comment: An error in the proof of Lemma 5.4 has been corrected |
| Databáze: | OpenAIRE |
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