随机块模型中巨分量顶点数的中心极限定理

关于巨分支阶数和k-核的中心极限定理的简短证明

A short proof of a central limit theorem for the order of the giant component and $k$-core

研究用新简单方法证图参数中心极限定理，利用埃弗龙 - 斯坦因不等式，经边重采样稳定性组合分析，给出稀疏随机图巨分支阶数和k-核中心极限定理简短证明。

Central limit theorem for linear spectral statistics of block-Wigner-type matrices

Motivated by the stochastic block model, we investigate a class of Wigner-type matrices with certain block structures, and establish a CLT for the corresponding linear spectral statistics via the large-deviation bounds from local law and the cumulant expansion formula. We apply the results to the stochastic block model. Specifically, a class of renormalized adjacency matrices will be block-Wigner-type matrices. Further, we show that for certain estimator of such renormalized adjacency matrices, which will be no longer Wigner-type but share long-range non-decaying weak correlations among the en…

Fluctuation results for general block spin Ising models

We study a block spin mean-field Ising model, i.e. a model of spins in which the vertices are divided into a finite number of blocks with each block having a fixed proportion of vertices, and where pair interactions are given according to their blocks. For the vector of block magnetizations we prove Large Deviation Principles and Central Limit Theorems under general assumptions for the block interaction matrix. Using the exchangeable pair approach of Stein's method we establish a rate of convergence in the Central Limit Theorem for the block magnetization vector in the high temperature regime.

Fluctuations for block spin Ising models

We analyze the high temperature fluctuations of the magnetization of the so-called Ising block model. This model was recently introduced by Berthet, Rigollet and Srivastava. We prove a Central Limit Theorems (CLT) for the magnetization in the high temperature regime. At the same time we show that this CLT breaks down at a line of critical temperatures. At this line we show the validity of a non-standard Central Limit Theorems for the magnetization.

非齐次随机图的微观与宏观泛函的泛函中心极限定理

Functional Central limit theorems for microscopic and macroscopic functionals of inhomogeneous random graphs

本文针对有限类型空间上的非齐次随机图，建立了微观类型密度和宏观巨分量观测量的泛函中心极限定理，并推广到最小生成树权重。

A Central Limit Theorem for non-overlapping return times

Define the non-overlapping return time of a random process to be the number of blocks that we wait before a particular block reappears. We prove a Central Limit Theorem based on these return times. This result has applications to entropy estimation, and to the problem of determining if digits have come from an independent equidistribted sequence. In the case of an equidistributed sequence, we use an argument based on negative association to prove convergence under weaker conditions.