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ON THE DISTRIBUTION OF THE LARGEST EIGENVALUE IN PRINCIPAL COMPONENTS ANALYSIS
LARGEST EIGENVALUE PRINCIPAL COMPONENTS
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2015/8/20
Let x1 denote the square of the largest singular value of an n × p
matrix X, all of whose entries are independent standard Gaussian varates. Equivalently, x1 is the largest principal component vari...
The Size of the Largest Part of Random Weighted Partitions of Large Integers
Random Weighted Partitions Large Integers Probability
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2011/9/20
Abstract: For a given sequence of weights (non-negative numbers), we consider partitions of the positive integer n. Each n-partition is selected uniformly at random from the set of all such partitions...
The largest eigenvalue of real symmetric, Hermitian and Hermitian self-dual random matrix models with rank one external source, part I
largest eigenvalue of real symmetric Hermitian and Hermitian self-dual random matrix rank one external source
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2011/2/22
We consider the limiting location and limiting distribution of the largest eigenvalue in real
symmetric (β = 1), Hermitian (β = 2), and Hermitian self-dual (β = 4) random matrix models
with rank 1 e...
Asymptotic Behaviors of The Size of The Largest Cluster in One Dimensional Percolation
The Largest Cluster One Dimensional Percolation
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2010/11/23
This paper focuses on the asymptotic behaviors of the length of the largest $1$-cluster in a finite iid Bernoulli sequence. We first reveal a critical phenomenon on the length and then study its limit...
On Jiang's asymptotic distribution of the largest entry of a sample correlation matrix
On Jiang's asymptotic distribution correlation matrix
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2010/11/19
Let $ \{X, X_{k,i}; i \geq 1, k \geq 1 \}$ be a double array of nondegenerate i.i.d. random variables and let $\{p_{n}; n \geq 1 \}$ be a sequence of positive integers such that $n/p_{n}$ is bounded a...
Largest Schmidt eigenvalue of entangled random pure states and conductance distribution in chaotic cavities
Largest Schmidt eigenvalue entangled random pure states conductance distribution
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2010/12/15
A strategy to evaluate the distribution of the largest Schmidt eigenvalue for entangled random pure states of bipartite systems is proposed. We point out that the multiple integral defining the sought...
Bounding an index by the largest character degree of a solvable group
Index Character Degree p-radical
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2010/12/14
In this paper, we show that if p is a prime and G is a p-solvable group, then |G: Op(G)|p (b(G)p/p)1/(p−1) where b(G) is the largest character degree of G. If p is an odd prime that is not a M...
Non-bipartite Graphs with Third Largest Laplacian Eigenvalue Less Than Three
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2007/12/12
All bipartite graphs whose third largest Laplacian eigenvalue is less than 3 have been characterized by Zhang. In this paper, all connected non-bipartite graphs with third largest Laplacian eigenvalue...
Optimal Preemptive Online Algorithms for Scheduling with Known Largest Size on two Uniform Machines
semi-online preemptive scheduling uniform machines competitive ratio
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2007/12/11
In this paper, we consider the semi-online preemptive scheduling problem with known largest job sizes on two uniform machines. Our goal is to maximize the continuous period of time (starting from time...
ON THE κ-th LARGEST EIGENVALUE OF THE LAPLACIAN MATRIX OF A GRAPH
Laplacian matrix eigenvalue
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2007/12/10
In this paper,we give the upper bound and lower bound of k-th largest eigenvalue λ_κ of the Laplacian matrix of a graph G in terms of the edge number of G and the number of spanning trees of G.