Toeplitz operators and zeros of square-integrable random holomorphic sections
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866916221396451328 |
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| author | Drewitz, Alexander Liu, Bingxiao Marinescu, George |
| author_facet | Drewitz, Alexander Liu, Bingxiao Marinescu, George |
| contents | We use the theory of abstract Wiener spaces to construct a probabilistic model for Berezin-Toeplitz quantization on a complete Hermitian complex manifold endowed with a positive line bundle. We associate to a function with compact support (a classical observable) a family of square-integrable Gaussian holomorphic sections. Our focus then is on the asymptotic distributions of their zeros in the semiclassical limit, in particular, we prove equidistribution results, large deviation estimates, and central limit theorems of the random zeros on the support of the given function. One of the key ingredients of our approach is the local asymptotic expansions of Berezin-Toeplitz kernels with non-smooth symbols. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_15983 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Toeplitz operators and zeros of square-integrable random holomorphic sections Drewitz, Alexander Liu, Bingxiao Marinescu, George Complex Variables Mathematical Physics 30C15, 32A60, 47B35, 53D50, 60D05 We use the theory of abstract Wiener spaces to construct a probabilistic model for Berezin-Toeplitz quantization on a complete Hermitian complex manifold endowed with a positive line bundle. We associate to a function with compact support (a classical observable) a family of square-integrable Gaussian holomorphic sections. Our focus then is on the asymptotic distributions of their zeros in the semiclassical limit, in particular, we prove equidistribution results, large deviation estimates, and central limit theorems of the random zeros on the support of the given function. One of the key ingredients of our approach is the local asymptotic expansions of Berezin-Toeplitz kernels with non-smooth symbols. |
| title | Toeplitz operators and zeros of square-integrable random holomorphic sections |
| topic | Complex Variables Mathematical Physics 30C15, 32A60, 47B35, 53D50, 60D05 |
| url | https://arxiv.org/abs/2404.15983 |