Search results for "NUMBER"
showing 10 items of 3939 documents
Central Limit Theorem for Linear Eigenvalue Statistics for a Tensor Product Version of Sample Covariance Matrices
2017
For $$k,m,n\in {\mathbb {N}}$$ , we consider $$n^k\times n^k$$ random matrices of the form $$\begin{aligned} {\mathcal {M}}_{n,m,k}({\mathbf {y}})=\sum _{\alpha =1}^m\tau _\alpha {Y_\alpha }Y_\alpha ^T,\quad {Y}_\alpha ={\mathbf {y}}_\alpha ^{(1)}\otimes \cdots \otimes {\mathbf {y}}_\alpha ^{(k)}, \end{aligned}$$ where $$\tau _{\alpha }$$ , $$\alpha \in [m]$$ , are real numbers and $${\mathbf {y}}_\alpha ^{(j)}$$ , $$\alpha \in [m]$$ , $$j\in [k]$$ , are i.i.d. copies of a normalized isotropic random vector $${\mathbf {y}}\in {\mathbb {R}}^n$$ . For every fixed $$k\ge 1$$ , if the Normalized Counting Measures of $$\{\tau _{\alpha }\}_{\alpha }$$ converge weakly as $$m,n\rightarrow \infty $$…
Rejoinder: Bayesian Checking of the Second Levels of Hierarchical Models
2008
Rejoinder: Bayesian Checking of the Second Levels of Hierarchical Models [arXiv:0802.0743]
Uncertainty in 2-point correlation function estimators and baryon acoustic oscillation detection in galaxy surveys
2012
Abstract We study the uncertainty in different two-point correlation function (2PCF) estimators in currently available galaxy surveys. This is motivated by the active subject of using the baryon acoustic oscillations (BAOs) feature in the correlation function as a tool to constrain cosmological parameters, which requires a fine analysis of the statistical significance. We discuss how estimators are affected by both the uncertainty in the mean density n and the integral constraint 1 V 2 ∫ V 2 ξ ˆ ( r ) d 3 r = 0 which necessarily causes a bias. We quantify both effects for currently available galaxy samples using simulated mock catalogues of the Sloan Digital Sky Survey (SDSS) following a lo…
Parallel Construction and Query of Index Data Structures for Pattern Matching on Square Matrices
1999
AbstractWe describe fast parallel algorithms for building index data structures that can be used to gather various statistics on square matrices. The main data structure is the Lsuffix tree, which is a generalization of the classical suffix tree for strings. Given ann×ntext matrixA, we build our data structures inO(logn) time withn2processors on a CRCW PRAM, so that we can quickly processAin parallel as follows: (i) report some statistical information aboutA, e.g., find the largest repeated square submatrices that appear at least twice inAor determine, for each position inA, the smallest submatrix that occurs only there; (ii) given, on-line, anm×mpattern matrixPAT, check whether it occurs i…
Estimating the geometric median in Hilbert spaces with stochastic gradient algorithms: Lp and almost sure rates of convergence
2016
The geometric median, also called L 1 -median, is often used in robust statistics. Moreover, it is more and more usual to deal with large samples taking values in high dimensional spaces. In this context, a fast recursive estimator has been introduced by Cardot et?al. (2013). This work aims at studying more precisely the asymptotic behavior of the estimators of the geometric median based on such non linear stochastic gradient algorithms. The L p rates of convergence as well as almost sure rates of convergence of these estimators are derived in general separable Hilbert spaces. Moreover, the optimal rates of convergence in quadratic mean of the averaged algorithm are also given.
How fair is an equitable distribution?
2006
Envy is a rather complex and irrational emotion. In general, it is very difficult to obtain a measure of this feeling, but in an economical context envy becomes an observable which can be measured. When various individuals compare their possessions, envy arises due to the inequality of their different allocations of commodities and different preferences. In this paper we show that an equitable distribution of goods does not guarantee a state of fairness between agents and in general that envy cannot be controlled by tuning the distribution of goods.
A dynamical approach to compatible and incompatible questions
2019
We propose a natural strategy to deal with compatible and incompatible binary questions, and with their time evolution. The strategy is based on the simplest, non-commutative, Hilbert space $\mathcal{H}=\mathbb{C}^2$, and on the (commuting or not) operators on it. As in ordinary Quantum Mechanics, the dynamics is driven by a suitable operator, the Hamiltonian of the system. We discuss a rather general situation, and analyse the resulting dynamics if the Hamiltonian is a simple Hermitian matrix.
On the empirical spectral distribution for certain models related to sample covariance matrices with different correlations
2021
Given [Formula: see text], we study two classes of large random matrices of the form [Formula: see text] where for every [Formula: see text], [Formula: see text] are iid copies of a random variable [Formula: see text], [Formula: see text], [Formula: see text] are two (not necessarily independent) sets of independent random vectors having different covariance matrices and generating well concentrated bilinear forms. We consider two main asymptotic regimes as [Formula: see text]: a standard one, where [Formula: see text], and a slightly modified one, where [Formula: see text] and [Formula: see text] while [Formula: see text] for some [Formula: see text]. Assuming that vectors [Formula: see t…
Topological Minimally Entangled States via Geometric Measure
2014
Here we show how the Minimally Entangled States (MES) of a 2d system with topological order can be identified using the geometric measure of entanglement. We show this by minimizing this measure for the doubled semion, doubled Fibonacci and toric code models on a torus with non-trivial topological partitions. Our calculations are done either quasi-exactly for small system sizes, or using the tensor network approach in [R. Orus, T.-C. Wei, O. Buerschaper, A. Garcia-Saez, arXiv:1406.0585] for large sizes. As a byproduct of our methods, we see that the minimisation of the geometric entanglement can also determine the number of Abelian quasiparticle excitations in a given model. The results in …
Duality and spatial inhomogeneity
2001
Within the framework on non-extensive thermostatistics we revisit the recently advanced q-duality concept. We focus our attention here on a modified q-entropic measure of the spatial inhomogeneity for binary patterns. At a fixed length-scale this measure exhibits a generalised duality that links appropriate pairs of q and q' values. The simplest q q' invariant function, without any free parameters, is deduced here. Within an adequate interval q < qo < q', in which the function reaches its maximum value at qo, this invariant function accurately approximates the investigated q-measure, nitidly evidencing the duality phenomenon. In the close vicinity of qo, the approximate meaningful rel…