标题： 非局部相互作用能量的粒子近似 显示英文标题

标题： Particle approximation of nonlocal interaction energies

摘要： 我们研究了具有通用相互作用核的Riesz型非局部能量及其与粒子系统的离散化。我们证明了离散化的能量在弱$*$拓扑下以$\Gamma$收敛到定义在概率测度空间上的Riesz泛函。我们还研究了离散化能量的最小化问题，并在非常一般且自然的设定下证明了粒子最小配置的存在性。 显示英文摘要

摘要： We consider Riesz-type nonlocal energies with general interaction kernels and their discretizations related to particle systems. We prove that the discretized energies $\Gamma$-converge in the weak-$*$ topology to the Riesz functional defined over the space of probability measures. We also address the minimization problem for the discretized energies, and prove the existence of minimal configurations of particles in a very general and natural setting.