论文标题
Schur补充的低调
Hypocoercivity with Schur complements
论文作者
论文摘要
我们提出了一种通过使用SCHUR补充，而不是从Evolution Semigroup的指数衰减与时间积分相结合的指数衰减中，提出了一种获得对低碳操作员分析的明确估计的方法。我们向类似Langevin的动力学和fokker-Planck方程以及线性玻尔兹曼方程（这也是分子动力学中随机混合蒙特卡洛的生成器）提出了应用。特别是，我们确切地确定了分解界限对动力学参数和维度的依赖性。我们还强调了我们的方法与其他低调方法的关系。
We propose an approach to obtaining explicit estimates on the resolvent of hypocoercive operators by using Schur complements, rather than from an exponential decay of the evolution semigroup combined with a time integral. We present applications to Langevin-like dynamics and Fokker--Planck equations, as well as the linear Boltzmann equation (which is also the generator of randomized Hybrid Monte Carlo in molecular dynamics). In particular, we make precise the dependence of the resolvent bounds on the parameters of the dynamics and on the dimension. We also highlight the relationship of our method with other hypocoercive approaches.
