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A Combinatorial Central Limit Theorem [PDF]

The Annals of Mathematical Statistics, 1951
Let (Y n1,…,Y nn be a random vector which takes on the n! permutations of (1,…, n) with equal probabilities. Let c n(i,j), i,j = 1, …, n, be n real numbers. Sufficient conditions for the asymptotic normality of $$ S_n = \sum\limits_{i - 1}^n {c_n \left( {i,Y_{ni} } \right)} $$ are given (Theorem 3). For the special case c n(i,j) = a n(i)b n(j) a
openaire   +3 more sources

Active Thermal Field Integration for Marangoni‐Driven Salt Rejection and Water Collection

Advanced Functional Materials, EarlyView.
A thermal gradient fabric (TGF) evaporator with an auxiliary active thermal field can simultaneously increase evaporation rates and achieve long‐term salt rejection. The auxiliary active thermal field is well integrated with solar energy to construct moderate, extensive, and circulating Marangoni flow for salt rejection.
Can Ge, Shuai Guo, Wei Li, Xunlong Zhang, Bin Chen, Xiao Feng, Shichang Yang, Duo Xu, Zhen Yu, Sai Kishore Ravi, Weilin Xu, Jian Fang, Swee Ching Tan   +12 more
wiley   +1 more source

A Functional Central Limit Theorem for Kernel Type Density Estimators

Austrian Journal of Statistics, 2016
Kernel type density estimators are studied for random fields. A functional central limit theorem in the space of square integrable functions is proved if the locations of observations become more and more dense in an increasing sequence of domains.
István Fazekas, Peter Filzmoser
doaj   +1 more source

Entropy and the Central Limit Theorem

The Annals of Probability, 1986
The author establishes a strengthened central limit theorem for densities showing monotone convergence in the sense of relative entropy. The relative entropy is defined by \[ D_ n=\int f(x) \log f(x)/\phi (x)dx \] where f is the density function of a random variable, X, with finite variance and \(\phi\) is the normal density with the same mean and ...
openaire   +3 more sources

Unique Performance Considerations for Printable Organic Semiconductor and Perovskite Radiation Detectors: Toward Consensus on Best Practice Evaluation

Advanced Functional Materials, EarlyView.
A lack of standard approaches for testing and reporting the performance of metal halide perovskites and organic semiconductor radiation detectors has resulted in inconsistent interpretation of performance parameters, impeding progress in the field. This Perspective recommends key metrics and experimental details, which are suggested for reporting in ...
Jessie A. Posar, Matthew Large, Andrea Ciavatti, Laura Basiricò, Beatrice Fraboni, Paul J. Sellin, Attila J. Mozer, Marco Petasecca, Matthew J. Griffith   +8 more
wiley   +1 more source

Local limit theorems in free probability theory

, 2010
In this paper, we study the superconvergence phenomenon in the free central limit theorem for identically distributed, unbounded summands. We prove not only the uniform convergence of the densities to the semicircular density but also their $L^p ...
Wang, Jiun-Chau
core   +1 more source

Quantum Emitters in Hexagonal Boron Nitride: Principles, Engineering and Applications

Advanced Functional Materials, EarlyView.
Quantum emitters in hexagonal boron nitride have emerged as a promising candidate for quantum information science. This review examines the fundamentals of these quantum emitters, including their level structures, defect engineering, and their possible chemical structures.
Thi Ngoc Anh Mai, Md Shakhawath Hossain, Nhat Minh Nguyen, Yongliang Chen, Chaohao Chen, Xiaoxue Xu, Quang Thang Trinh, Toan Dinh, Toan Trong Tran   +8 more
wiley   +1 more source

Low‐Symmetry Weyl Semimetals: A Path to Ideal Topological States

Advanced Functional Materials, EarlyView.
This study presents a theoretical framework for realizing ideal Weyl semimetals, where Weyl nodes are well‐isolated at the Fermi level. The approach is exemplified in the low‐symmetry material Cu2SnSe3, which exhibits tunable topological phases, current‐induced orbital magnetization, and a strong circular photogalvanic effect, making it a promising ...
Darius‐Alexandru Deaconu, Varun Shah, Rodion Vladimirovich Belosludov, Mohammad Saeed Bahramy   +3 more
wiley   +1 more source

Convergence of Weighted Linear Process for ρ-Mixing Random Variables

Discrete Dynamics in Nature and Society, 2007
A central limit theorem and a functional central limit theorem are obtained for weighted linear process of ρ-mixing sequences for the Xt=∑i=0∞aiYt−i, where {Yi, 0 ...
Guang-Hui Cai
doaj   +1 more source

Wavelength‐Dependent Differential Amplification of Raman Scattering by Chiral Gold Nanorods for Multiplexed Encoding

Advanced Functional Materials, EarlyView.
The SERS spectra of reporter molecules adsorbed on chiral gold nanorods depends on the handedness of circularly polarized light (CPL‐SERS). The bisignate plasmonic CD spectra of chiral nanorods provides wavelength‐dependent CPL‐SERS. Selective discrimination of chiral nanorod handedness and different Raman reporters allow highly sensitive codification ...
Andrés Serrano‐Freijeiro, Carlos Renero‐Lecuna, Manuel Obelleiro‐Liz, Víctor F. Martín, Diptesh Dey, José M. Taboada, George C. Schatz, Isabel Pastoriza‐Santos, Jorge Pérez‐Juste, Luis M. Liz‐Marzán   +9 more
wiley   +1 more source