CYCLES AND EIGENVALUES OF SEQUENTIALLY GROWING RANDOM REGULAR GRAPHS
成果类型：
Article
署名作者：
Johnson, Tobias; Pal, Soumik
署名单位：
University of Washington; University of Washington Seattle
刊物名称：
ANNALS OF PROBABILITY
ISSN/ISSBN：
0091-1798
DOI：
10.1214/13-AOP864
发表日期：
2014
页码：
1396-1437
关键词：
摘要：
Consider the sum of d many i.i.d. random permutation matrices on n labels along with their transposes. The resulting matrix is the adjacency matrix of a random regular (multi)-graph of degree 2d on n vertices. It is known that the distribution of smooth linear eigenvalue statistics of this matrix is given asymptotically by sums of Poisson random variables. This is in contrast with Gaussian fluctuation of similar quantities in the case of Wigner matrices. It is also known that for Wigner matrices the joint fluctuation of linear eigenvalue statistics across minors of growing sizes can be expressed in terms of the Gaussian Free Field (GFF). In this article, we explore joint asymptotic (in n) fluctuation for a coupling of all random regular graphs of various degrees obtained by growing each component permutation according to the Chinese Restaurant Process. Our primary result is that the corresponding eigenvalue statistics can be expressed in terms of a family of independent Yule processes with immigration. These processes track the evolution of short cycles in the graph. If we now take d to infinity, certain GFF-like properties emerge.
来源URL：