A Stochastic Variant of the Abelian Sandpile Model
A Stochastic Variant of the Abelian Sandpile Model
复制标题
阿贝尔沙堆模型的随机变体
DOI：
10.1007/s10955-019-02453-7
复制
发表时间：
2020
影响因子：
1.6
通讯作者：
Yuntao Wang
中科院分区：
文献类型：
--
作者：
Seungki Kim;Yuntao Wang
我们介绍了一个自然的随机扩展，称为SSP，阿贝尔沙堆模型（ASM），它与ASM共享许多数学属性，但从根本上不同的物理行为，例如在稳态的形状和雪崩的大小分布。我们建立了一个类似于ASM的SSP的基本理论，并对其行为进行了简要的数值研究。我们研究SSP的最初动机源于它与Ding等人在另一项工作中建立的LLL算法的联系（LLL和随机沙堆模型，https：//sites.google.com/view/seungki/）。理解LLL如何工作的重要性不能再强调了，特别是从基于格的密码学的角度来看。我们相信SSP可以作为一个易于处理的LLL玩具模型，这将有助于我们进一步了解它。
We introduce a natural stochastic extension, calledSSP, of the abelian sandpile model (ASM), which shares many mathematical properties with ASM, yet radically differs in its physical behavior, for example in terms of the shape of the steady state and of the avalanche size distribution. We establish a basic theory of SSP analogous to that of ASM, and present a brief numerical study of its behavior. Our original motivation for studying SSP stems from its connection to the LLL algorithm established in another work by Ding et al. (LLL and stochastic sandpile models, https://sites.google.com/view/seungki/). The importance of understanding how LLL works cannot be stressed more, especially from the point of view of lattice-based cryptography. We believe SSP serves as a tractable toy model of LLL that would help further our understanding of it.