Report
On the derivation of the homogeneous kinetic wave equation for a nonlinear random matrix model
| العنوان: | On the derivation of the homogeneous kinetic wave equation for a nonlinear random matrix model |
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| المؤلفون: | Dubach, Guillaume, Germain, Pierre, Harrop-Griffiths, Benjamin |
| المصدر: | Ars Inveniendi Analytica (2023), Paper No. 7, 63 pp |
| سنة النشر: | 2022 |
| المجموعة: | Mathematics Mathematical Physics |
| مصطلحات موضوعية: | Mathematics - Analysis of PDEs, Mathematical Physics, Mathematics - Probability |
| الوصف: | We consider a nonlinear system of ODEs, where the underlying linear dynamics are determined by a Hermitian random matrix ensemble. We prove that the leading order dynamics in the weakly nonlinear, infinite volume limit are determined by a solution to the corresponding kinetic wave equation on a non-trivial timescale. Our proof relies on estimates for Haar-distributed unitary matrices obtained from Weingarten calculus, which may be of independent interest. Comment: 63 pages, 15 figures |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2203.13748 |
| رقم الانضمام: | edsarx.2203.13748 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |