scholarly journals Spectral statistics for one-dimensional Anderson model with unbounded but decaying potential

2019 ◽  
Vol 22 (02) ◽  
pp. 1950012
Author(s):  
Anish Mallick ◽  
Dhriti Ranjan Dolai
Keyword(s):  
Anderson Model ◽  
Random Variables ◽  
Single Site ◽  
Symmetric Distribution ◽  
One Dimensional ◽  
Site Distribution ◽  
Fat Tail ◽  
Spectral Statistics

In this work, we study the spectral statistics for Anderson model on [Formula: see text] with decaying randomness whose single-site distribution has unbounded support. Here, we consider the operator [Formula: see text] given by [Formula: see text], [Formula: see text] and [Formula: see text] are real i.i.d random variables following symmetric distribution [Formula: see text] with fat tail, i.e. [Formula: see text] for [Formula: see text], for some constant [Formula: see text]. In case of [Formula: see text], we are able to show that the eigenvalue process in [Formula: see text] is the clock process.

scholarly journals From closed to open one-dimensional Anderson model: Transport versus spectral statistics

2012 ◽  
Vol 86 (1) ◽  
Author(s):  
S. Sorathia ◽  
F. M. Izrailev ◽  
V. G. Zelevinsky ◽  
G. L. Celardo
Keyword(s):  
Anderson Model ◽  
One Dimensional ◽  
Spectral Statistics

scholarly journals LOCALIZED ENTANGLEMENT IN ONE-DIMENSIONAL ANDERSON MODEL

2005 ◽  
Vol 19 (11) ◽  
pp. 517-527 ◽  
Author(s):  
HAIBIN LI ◽  
XIAOGUANG WANG
Keyword(s):  
Anderson Model ◽  
Localization Length ◽  
Direct Relation ◽  
Disorder Strength ◽  
One Dimensional ◽  
Entanglement Distribution ◽  
Localization Center

The entanglement in one-dimensional Anderson model is studied. The pairwise entanglement has a direct relation to the localization length and is reduced by disorder. Entanglement distribution displays the entanglement localization. The pairwise entanglements around localization center exhibit a maximum as the disorder strength increases. The dynamics of entanglement are also investigated.

scholarly journals Fat Tail Model for Simulating Test Systems in Multiperiod Unit Commitment

2015 ◽  
Vol 2015 ◽  
pp. 1-7 ◽  
Author(s):  
J. A. Marmolejo ◽  
R. Rodriguez
Keyword(s):  
Power Systems ◽  
Unit Commitment ◽  
Electrical Power ◽  
Random Variables ◽  
Production Costs ◽  
Unit Commitment Problem ◽  
Test Systems ◽  
Fat Tail ◽  
Commitment Problem ◽  
Stable Random Variables

This paper describes the use of Chambers-Mallows-Stuck method for simulating stable random variables in the generation of test systems for economic analysis in power systems. A study that focused on generating test electrical systems through fat tail model for unit commitment problem in electrical power systems is presented. Usually, the instances of test systems in Unit Commitment are generated using normal distribution, but in this work, simulations data are based on a new method. For simulating, we used three original systems to obtain the demand behavior and thermal production costs. The estimation of stable parameters for the simulation of stable random variables was based on three generally accepted methods: (a) regression, (b) quantiles, and (c) maximum likelihood, choosing one that has the best fit of the tails of the distribution. Numerical results illustrate the applicability of the proposed method by solving several unit commitment problems.

Dependent Random Variables with Independent Subsets - II

1990 ◽  
Vol 33 (1) ◽  
pp. 24-28 ◽  
Author(s):  
Y. H. Wang
Keyword(s):  
Joint Distribution ◽  
Random Variables ◽  
Marginal Distributions ◽  
Dependent Random Variables ◽  
One Dimensional ◽  
The One

AbstractIn this paper, we consolidate into one two separate problems - dependent random variables with independent subsets and construction of a joint distribution with given marginals. Let N = {1,2,3,...} and X = {Xn; n ∊ N} be a sequence of random variables with nondegenerate one-dimensional marginal distributions {Fn; n ∊ N}. An example is constructed to show that there exists a sequence of random variables Y = {Yn; n ∊ N} such that the components of a subset of Y are independent if and only if its size is ≦ k, where k ≧ 2 is a prefixed integer. Furthermore, the one-dimensional marginal distributions of Y are those of X.

scholarly journals Estimating Differential Entropy using Recursive Copula Splitting

Entropy ◽  
2020 ◽  
Vol 22 (2) ◽  
pp. 236 ◽  
Author(s):  
Gil Ariel ◽  
Yoram Louzoun
Keyword(s):  
Compact Support ◽  
Mixed Type ◽  
Random Variables ◽  
Differential Entropy ◽  
High Dimensions ◽  
Marginal Distributions ◽  
Numerical Examples ◽  
One Dimensional ◽  
Different Dimensions

A method for estimating the Shannon differential entropy of multidimensional random variables using independent samples is described. The method is based on decomposing the distribution into a product of marginal distributions and joint dependency, also known as the copula. The entropy of marginals is estimated using one-dimensional methods. The entropy of the copula, which always has a compact support, is estimated recursively by splitting the data along statistically dependent dimensions. The method can be applied both for distributions with compact and non-compact supports, which is imperative when the support is not known or of a mixed type (in different dimensions). At high dimensions (larger than 20), numerical examples demonstrate that our method is not only more accurate, but also significantly more efficient than existing approaches.

A one dimensional random space-filling problem

1968 ◽  
Vol 5 (02) ◽  
pp. 427-435 ◽  
Author(s):  
John P. Mullooly
Keyword(s):  
Asymptotic Behavior ◽  
Finite Number ◽  
Real Line ◽  
Random Variables ◽  
Random Interval ◽  
Space Filling ◽  
One Dimensional ◽  
The Real ◽  
Fixed Constant ◽  
Filling Problem

Consider an interval of the real line (0, x), x > 0; and place in it a random subinterval S(x) defined by the random variables Xx and Yx , the position of the center of S(x) and the length of S(x). The set (0, x)– S(x) consists of two intervals of length δ and η. Let a > 0 be a fixed constant. If δ ≦ a, then a random interval S(δ) defined by Xδ, Yδ is placed in the interval of length δ. If δ < a, the placement of the second interval is not made. The same is done for the interval of length η. Continue to place non-intersecting random subintervals in (0, x), and require that the lengths of all the random subintervals be ≦ a. The process terminates after a finite number of steps when all the segments of (0, x) uncovered by random subintervals are of length < a. At this stage, we say that (0, x) is saturated. Define N(a, x) as the number of random subintervals that have been placed when the process terminates. We are interested in the asymptotic behavior of the moments of N(a, x), for large x.

Sign in / Sign up

Export Citation Format

Share Document