论文标题
随机步行在水晶晶格和多个Zeta功能上
Random walks on crystal lattices and multiple zeta functions
论文作者
论文摘要
已知晶格是经典周期晶格的概括之一，可以正确嵌入一些欧几里得空间中。为了使欧几里得空间上的多种多维离散分布更具治疗性，多维欧拉产物和多维shintani zeta功能在晶体晶格上引入。它们与现有的Ihara Zeta函数完全不同，因为我们的Zeta功能直接在晶体晶格上定义。通过定期实现晶体晶格的概念，我们可以明确地提供多种多维离散分布。特别是，随机步行在范围是无限的晶格上，其范围有限的随机步行是由多维欧拉产物和多维的shintani zeta函数构建的。我们还提供了一些可理解的例子。
Crystal lattices are known to be one of the generalizations of classical periodic lattices which can be embedded into some Euclidean spaces properly. As to make a wide range of multidimensional discrete distributions on Euclidean spaces more treatable, multidimensional Euler products and multidimensional Shintani zeta functions on crystal lattices are introduced. They are completely different from existing Ihara zeta functions on graphs in that our zeta functions are defined on crystal lattices directly. Via a concept of periodic realizations of crystal lattices, we make it possible to provide many kinds of multidimensional discrete distributions explicitly. In particular, random walks on crystal lattices whose range is infinite and such random walks whose range is finite are constructed by multidimensional Euler products and multidimensional Shintani zeta functions, respectively. We give some comprehensible examples as well.
