论文标题
随机矩阵凝聚力的本地和全球普遍性
Local and global universality of random matrix cokernels
论文作者
论文摘要
在本文中，我们研究了各种随机积分矩阵模型的焦点，包括随机对称，随机偏斜 - 对称和随机拉普拉斯矩阵。我们提供了一种系统的方法来建立在非常一般的随机性假设下的普遍性。我们的亮点包括所有这些模型的Cokernel统计数据的本地和全球通用性。特别是，我们发现Erdos-Renyi随机图的沙珀斯组是循环的，从2008年开始回答了洛伦齐尼的问题。
In this paper we study the cokernels of various random integral matrix models, including random symmetric, random skew-symmetric, and random Laplacian matrices. We provide a systematic method to establish universality under very general randomness assumption. Our highlights include both local and global universality of the cokernel statistics of all these models. In particular, we find the probability that a sandpile group of an Erdos-Renyi random graph is cyclic, answering a question of Lorenzini from 2008.
