Concentration properties of Gaussian random fields
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arXiv
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| Format: | Preprint |
| Publié: |
2014
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| _version_ | 1866913258628186112 |
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| author | Sharma, Gargee |
| author_facet | Sharma, Gargee |
| contents | We study the problem of a random Gaussian vector field given that a particular real quadratic form $\mathcal{Q}$ is arbitrarily large. We prove that in such a case the Gaussian field is primarily governed by the fundamental eigenmode of a particular operator. As a good check of our proposition we use it to re-derive the result of Adler dealing with the structure of field in the vicinity of a high local maxima. We have also applied our result to an incompressible homogeneous Gaussian random flow in the limit of large local helicity and calculate the structure of the flow. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1404_7424 |
| institution | arXiv |
| publishDate | 2014 |
| record_format | arxiv |
| spellingShingle | Concentration properties of Gaussian random fields Sharma, Gargee Mathematical Physics Disordered Systems and Neural Networks We study the problem of a random Gaussian vector field given that a particular real quadratic form $\mathcal{Q}$ is arbitrarily large. We prove that in such a case the Gaussian field is primarily governed by the fundamental eigenmode of a particular operator. As a good check of our proposition we use it to re-derive the result of Adler dealing with the structure of field in the vicinity of a high local maxima. We have also applied our result to an incompressible homogeneous Gaussian random flow in the limit of large local helicity and calculate the structure of the flow. |
| title | Concentration properties of Gaussian random fields |
| topic | Mathematical Physics Disordered Systems and Neural Networks |
| url | https://arxiv.org/abs/1404.7424 |