Lindeberg原理的推广

Polynomial chaos and scaling limits of disordered systems

Inspired by recent work of Alberts, Khanin and Quastel, we formulate general conditions ensuring that a sequence of multi-linear polynomials of independent random variables (called polynomial chaos expansions) converges to a limiting random variable, given by a Wiener chaos expansion over the d-dimensional white noise. A key ingredient in our approach is a Lindeberg principle for polynomial chaos expansions, which extends earlier work of Mossel, O'Donnell and Oleszkiewicz. These results provide a unified framework to study the continuum and weak disorder scaling limits of statistical mechanics…

Maximum Relative Divergence Principle for Grading Functions on Power Sets

The concept of Relative Divergence of one Grading Function from another is extended from totally ordered chains to power sets of finite event spaces. Shannon Entropy concept is extended to normalized grading functions on such power sets. Maximum Relative Divergence Principle is introduced as a generalization of the Maximum Entropy Principle as a tool for determining the "most reasonable" grading function and used in some Operations Research applications where that function is supposed to be "element-additive" or "cardinality-dependent" under application-specific linear constraints.

分数布朗单的一个不变原理

An invariance principle for fractional Brownian sheets

建立了具有相依新息的平稳线性随机场部分和的中心极限定理和各向异性分数布朗单的不变原理。我们的结果是Dedecker等人（2011）的分数布朗运动的不变原理在高维的推广。他们的论点的一个关键组成部分，鞅近似，被替换为m-近似参数。我们的方法的一个重要工具是最近由El Machkouri et al.（2011）建立的平稳随机场的矩不等式。

$\ell^{\infty}$ Poisson invariance principles from two classical Poisson limit theorems and extension to non-stationary independent sequences

The simple Lévy Poisson process and scaled forms are explicitly constructed from partial sums of independent and identically distributed random variables and from sums of non-stationary independent random variables. For the latter, the weak limits are scaled Poisson processes. The method proposed here prepares generalizations to dependent data, to associated data in the first place.

A Moment Majorization principle for random matrix ensembles

We prove a moment majorization principle for matrix-valued functions with domain $\{-1,1\}^{m}$, $m\in\mathbb{N}$. The principle is an inequality between higher-order moments of a non-commutative multilinear polynomial with different random matrix ensemble inputs, where each variable has small influence and the variables are instantiated independently. This technical result can be interpreted as a noncommutative generalization of one of the two inequalities of the seminal invariance principle of Mossel, O'Donnell and Oleszkiewicz. Applications to noncommutative noise stability and noncommutati…