تقرير
Explicit convergence rates of underdamped Langevin dynamics under weighted and weak Poincar\'e--Lions inequalities
| العنوان: | Explicit convergence rates of underdamped Langevin dynamics under weighted and weak Poincar\'e--Lions inequalities |
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| المؤلفون: | Brigati, Giovanni, Stoltz, Gabriel, Wang, Andi Q., Wang, Lihan |
| سنة النشر: | 2024 |
| المجموعة: | Mathematics Statistics |
| مصطلحات موضوعية: | Mathematics - Probability, Mathematics - Analysis of PDEs, Statistics - Computation |
| الوصف: | We study the long-time convergence behavior of underdamped Langevin dynamics, when the spatial equilibrium satisfies a weighted Poincar\'e inequality, with a general velocity distribution, which allows for fat-tail or subexponential potential energies, and provide constructive and fully explicit estimates in $\mathrm{L}^2$-norm with $\mathrm{L}^\infty$ initial conditions. A key ingredient is a space-time weighted Poincar\'e--Lions inequality, which in turn implies a weak Poincar\'e--Lions inequality. Comment: This is a preliminary version of the work. The proofs are complete, but we will reorganize and polish the manuscript before submitting to a journal. Comments are welcome! |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2407.16033 |
| رقم الأكسشن: | edsarx.2407.16033 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |