论文标题
Ronkin/Zeta对应
Ronkin/Zeta Correspondence
论文作者
论文摘要
在考虑几乎周期性函数的零时，Ronkin的定义了Ronkin函数。最近，该功能已用于数学，物理等各个研究领域。尤其是在数学中，它与热带几何形状，变形虫，牛顿多面体和二聚体模型具有封闭的连接。 另一方面，我们已经对我们进行了一类新的Zeta功能，用于各种步行，包括量子步行，这是我们先前关于Zeta通信的一系列工作。量子步行是随机步行的量子对应物。在本文中，我们在随机步行和量子步行中提出了Ronkin功能与我们的Zeta功能之间的新关系。首先，在一维随机步行的情况下，我们认为这种关系。之后，我们处理高维随机步行。为了与量子步行的情况进行比较，我们还处理了一维量子步行的情况。我们的结果首次通过量子步行在Ronkin函数和Zeta功能之间的桥梁。
The Ronkin function was defined by Ronkin in the consideration of the zeros of almost periodic function. Recently, this function has been used in various research fields in mathematics, physics and so on. Especially in mathematics, it has a closed connections with tropical geometry, amoebas, Newton polytopes and dimer models. On the other hand, we have been investigated a new class of zeta functions for various kinds of walks including quantum walks by a series of our previous work on Zeta Correspondence. The quantum walk is a quantum counterpart of the random walk. In this paper, we present a new relation between the Ronkin function and our zeta function for random walks and quantum walks. Firstly we consider this relation in the case of one-dimensional random walks. Afterwards we deal with higher-dimensional random walks. For comparison with the case of the quantum walk, we also treat the case of one-dimensional quantum walks. Our results bridge between the Ronkin function and the zeta function via quantum walks for the first time.
