论文标题
分散的近似值的近似值，以扩散与整个riemannian歧管上的漂移和杀戮
A graph discretized approximation of semigroups for diffusion with drift and killing on a complete Riemannian manifold
论文作者
论文摘要
在本文中，我们证明了由Schrödinger运营商生成的$ C_ {0} $ - 在完整的Riemannian歧管上漂移而产生的$ C_ {0} $ - 由与离散时间随机步行相关的离散半群近似近似，该段是随机随机随机步行，并在一系列亲图中杀死，该序列是由统治图中构建的，该序列是由分区构建的。此外，当歧管紧凑时，我们还获得了收敛性的定量误差估计。最后，我们在两个典型的歧管上给出了歧管分区和漂移项的示例：欧几里得空间和模型歧管。
In the present paper, we prove that the $C_{0}$-semigroup generated by a Schrödinger operator with drift on a complete Riemannian manifold is approximated by the discrete semigroups associated with a family of discrete time random walks with killing in a flow on a sequence of proximity graphs, which are constructed by partitions of the manifold. Furthermore, when the manifold is compact, we also obtain a quantitative error estimate of the convergence. Finally, we give examples of the partition of the manifold and the drift term on two typical manifolds: Euclidean spaces and model manifolds.
