论文标题
在多维热带系列上缩小动态
Shrinking dynamic on multidimensional tropical series
论文作者
论文摘要
我们定义了多维热带系列，即在本地是热带多项式的分段线性函数，但可能包含无限数量的单一元素。热带系列出现在pluriharmonic功能的生长研究中。但是，我们的动机源于沙珀模型，其中某些波动动态控制沙子的行为并表现出权力定律（到目前为止，仅实验证据）。在本文中，我们在多维环境中为热带系列和相应的热带分析性超曲面奠定了基础。研究的主要对象是$ω$ - 热带系列，其中$ω$是一个紧凑的凸域，可以将其视为此类系列的收敛区域。 我们的主要定理是，通过给定有限的点产生$ω$ - 热带分析性超表面的沙珀动力学总是会稍微扰动，因此中级$ω$ - 热带分析性超浮标只有轻度的奇异性。
We define multidimensional tropical series, i.e. piecewise linear functions which are tropical polynomials locally but may contain an infinite number of monomials. Tropical series appeared in the study of the growth of pluriharmonic functions. However, our motivation stems from sandpile models where certain wave dynamic governs the behavior of sand and exhibits a power law (so far only experimental evidence). In this paper we lay the groundwork for tropical series and corresponding tropical analytical hypersurfaces in the multidimensional setting. The main object of study is an $Ω$-tropical series where $Ω$ is a compact convex domain which can be thought of as the region of convergence of such a series. Our main theorem is that the sandpile dynamics producing an $Ω$-tropical analytical hypersurface passing through a given finite set of points can always be slightly perturbed so that the intermediate $Ω$-tropical analytical hypersurfaces have only mild singularities.
