Super-Gaussian Decay of Exponentials: A Sufficient Condition
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arXiv
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| Format: | Preprint |
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2022
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| _version_ | 1866912215341203456 |
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| author | Hinrichs, Benjamin Janssen, Daan Willem Ziebell, Jobst |
| author_facet | Hinrichs, Benjamin Janssen, Daan Willem Ziebell, Jobst |
| contents | In this article, we present a sufficient condition for the exponential $\exp({-f})$ to have a tail decay stronger than any Gaussian, where $f$ is defined on a locally convex space $X$ and grows faster than a squared seminorm on $X$. In particular, our result proves that $\exp({-p(x)^{2+\varepsilon}+αq(x)^2})$ is integrable for all $α,\varepsilon>0$ w.r.t. a Radon Gaussian measure on a nuclear space $X$, if $p$ and $q$ are continuous seminorms on $X$ with compatible kernels. This can be viewed as an adaptation of Fernique's theorem and, for example, has applications in quantum field theory. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2205_09189 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Super-Gaussian Decay of Exponentials: A Sufficient Condition Hinrichs, Benjamin Janssen, Daan Willem Ziebell, Jobst Functional Analysis In this article, we present a sufficient condition for the exponential $\exp({-f})$ to have a tail decay stronger than any Gaussian, where $f$ is defined on a locally convex space $X$ and grows faster than a squared seminorm on $X$. In particular, our result proves that $\exp({-p(x)^{2+\varepsilon}+αq(x)^2})$ is integrable for all $α,\varepsilon>0$ w.r.t. a Radon Gaussian measure on a nuclear space $X$, if $p$ and $q$ are continuous seminorms on $X$ with compatible kernels. This can be viewed as an adaptation of Fernique's theorem and, for example, has applications in quantum field theory. |
| title | Super-Gaussian Decay of Exponentials: A Sufficient Condition |
| topic | Functional Analysis |
| url | https://arxiv.org/abs/2205.09189 |