Report
Gaussian holomorphic sections on noncompact complex manifolds
| العنوان: | Gaussian holomorphic sections on noncompact complex manifolds |
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| المؤلفون: | Drewitz, Alexander, Liu, Bingxiao, Marinescu, George |
| سنة النشر: | 2023 |
| المجموعة: | Mathematics Mathematical Physics |
| مصطلحات موضوعية: | Mathematics - Complex Variables, Mathematical Physics, Mathematics - Probability, 32A60, 60D05, 32U40, 60B12, 53D50 |
| الوصف: | We give two constructions of Gaussian-like random holomorphic sections of a Hermitian holomorphic line bundle $(L,h_{L})$ on a Hermitian complex manifold $(X,\Theta)$. In particular, we are interested in the case where the space of $\mathcal{L}^2$-holomorphic sections $H^{0}_{(2)}(X,L)$ is infinite dimensional. We first provide a general construction of Gaussian random holomorphic sections of $L$, which, if $\dim H^{0}_{(2)}(X,L)=\infty$, are almost never $\mathcal{L}^2$-integrable on $X$. The second construction combines the abstract Wiener space theory with the Berezin-Toeplitz quantization and yields a random $\mathcal{L}^2$-holomorphic section. Furthermore, we study their random zeros in the context of semiclassical limits, including their equidistribution, large deviation estimates and hole probabilities. Comment: 47 pages |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2302.08426 |
| رقم الانضمام: | edsarx.2302.08426 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |