Random Multiplication Approaches Uniform Measure in Finite Groups

所有1-Meixner随机向量的显式描述

Explicit descriptions of all 1-Meixner random vectors

针对具有各阶有限矩的1-Meixner随机向量，其联合半量子算子与乘法算子的交换子满足特定线性组合性质，本文推导了对应一阶偏微分方程组在任意维度下的所有解的显式描述。

随机乘法与随机和：具有整数值随机输入的类自回归模型

Random multiplication versus random sum: auto-regressive-like models with integer-valued random inputs

本文提出基于随机乘法算子的RMINAR整数值时间序列模型，证明其解处处严平稳遍历，并给出四阶段加权最小二乘估计及理论性质。

泊松乘法公式

The Poisson Multiplication Formula

本文建立了有限Wiener混沌中泊松泛函乘积平方可积的充分必要条件，通过迭代加一成本算子和新型Poincaré不等式得出泊松空间的一般乘法公式，解决了Surgailis（1984）的遗留问题。

Random motion on finite rings, I: commutative rings

We consider irreversible Markov chains on finite commutative rings randomly generated using both addition and multiplication. We restrict ourselves to the case where the addition is uniformly random and multiplication is arbitrary. We first prove formulas for eigenvalues and multiplicities of the transition matrices of these chains using the character theory of finite abelian groups. The examples of principal ideal rings (such as $\mathbb{Z}_{n}$) and finite chain rings (such as $\mathbb{Z}_{p^k}$) are particularly illuminating and are treated separately. We then prove a recursive formula for …

Uniform Modulus of Continuity of Random Fields

A sufficient condition for the uniform modulus of continuity of a random field $X = \{X(t), t \in \R^N\}$ is provided. The result is applicable to random fields with heavy-tailed distribution such as stable random fields.

$γ$-variable first-order logic of uniform attachment random graphs

We study logical limit laws for uniform attachment random graphs. In this random graph model, vertices and edges are introduced recursively: at time $n+1$, the vertex $n+1$ is introduced together with $m$ edges joining the new vertex with $m$ different vertices chosen uniformly at random from $1,\ldots,n$. We prove that this random graph obeys convergence law for first-order sentences with at most $m-2$ variables.

The Uniform Law for Sojourn Measures of Random Fields

The uniform law for sojourn times of processes with cyclically exchangeable increments is extended to the case of random fields, with general parameter sets, that possess a suitable invariance property.

A Note on Uniform Integrability of Random Variables in a Probability Space and Sublinear Expectation Space

In this note we discuss uniform integrability of random variables. In a probability space, we introduce two new notions on uniform integrability of random variables, and prove that they are equivalent to the classic one. In a sublinear expectation space, we give de La Vallée Poussin criterion for the uniform integrability of random variables and do some other discussions.

Random walks with unbounded jumps among random conductances I: Uniform quenched CLT

We study a one-dimensional random walk among random conductances, with unbounded jumps. Assuming the ergodicity of the collection of conductances and a few other technical conditions (uniform ellipticity and polynomial bounds on the tails of the jumps) we prove a quenched \textit{uniform} invariance principle for the random walk. This means that the rescaled trajectory of length $n$ is (in a certain sense) close enough to the Brownian motion, uniformly with respect to the choice of the starting location in an interval of length $O(\sqrt{n})$ around the origin.

Absolute Continuity and Weak Uniform Mixing of Random Walk in Dynamic Random Environment

We prove results for random walks in dynamic random environments which do not require the strong uniform mixing assumptions present in the literature. We focus on the "environment seen from the walker"-process and in particular its invariant law. Under general conditions it exists and is mutually absolutely continuous to the environment law. With stronger assumptions we obtain for example uniform control on the density or a quenched CLT. The general conditions are made more explicit by looking at hidden Markov models or Markov chains as environment and by providing simple examples.

均匀圆随机覆盖问题的一些确定结果

Certain results on uniform circle random covering problems

本文扩展了均匀圆随机覆盖问题中来自文献[13]的一个定理。

Distinguishing power-law uniform random graphs from inhomogeneous random graphs through small subgraphs

We investigate the asymptotic number of induced subgraphs in power-law uniform random graphs. We show that these induced subgraphs appear typically on vertices with specific degrees, which are found by solving an optimization problem. Furthermore, we show that this optimization problem allows to design a linear-time, randomized algorithm that distinguishes between uniform random graphs and random graph models that create graphs with approximately a desired degree sequence: the power-law rank-1 inhomogeneous random graph. This algorithm uses the fact that some specific induced subgraphs appear …

弱依赖随机变量的非均匀Berry-Esseen定理

Non-uniform Berry-Esseen theorems for weakly dependent random variables

本文研究弱依赖序列的非均匀Berry-Esseen估计，涵盖均匀椭圆非齐马克诺夫链、随机时间变化的弱混沌动力系统、随机矩阵乘积及局部统计等类别。

高斯随机变量三次方的特征函数

The Characteristic Function of the Cube of a Gaussian Random Variable

本文利用 $L^2(\mathbb{R},\mathbb{C})$ 的 Schwartz 类上乘法算子的谱分解，计算了高斯随机变量三次方的特征函数。

随机场的博雷尔变换的分布一致连续性

Uniform Continuity in Distribution for Borel Transformations of Random Fields

本文提供了随机场博雷尔变换分布一致连续性的简单充分条件。

An O(n) algorithm for generating uniform random vectors in n-dimensional cones

Unbiased random vectors i.e. distributed uniformly in n-dimensional space, are widely applied and the computational cost of generating a vector increases only linearly with n. On the other hand, generating uniformly distributed random vectors in its subspaces typically involves the inefficiency of rejecting vectors falling outside, or re-weighting a non-uniformly distributed set of samples. Both approaches become severely ineffective as n increases. We present an efficient algorithm to generate uniformly distributed random directions in n-dimensional cones, to aid searching and sampling tasks …