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Entropy and random feedback
Convex function matrix spectrum application linear controller design
2015/8/11
The gamma-entropy is a convex function of matrices that is closely related to the Frobenius and spectral (maximum singular value) norms. It comes up in several applications such as central H-infinity ...
Asymptotics of the Solutions of the Random Schrödinger Equation
Asymptotics of the Solutions Random Schrö dinger Equation
2015/7/14
We consider solutions of the Schrödinger equation with a weak time-dependent random potential. It is shown that when the two-point correlation function of the potential is rapidly decaying, then ...
Iterated Random Functions
Markov chains products of random matrices iterated function systems coupling from the past
2015/7/14
Iterated random functions are used to draw pictures or simulate large Ising models, among
other applications. They o er a method for studying the steady state distribution of a
Markov chain, and giv...
Linear Functionals of Eigenvalues of Random Matrices
Random unitary matrix the calculation function
2015/7/14
.L.et 1% be a random r~x r~unitary matrix with distribution given
by Haar measure on the unitary group. Using explicit monlerlt calculations,
a general criterion is given for linear cornbinations of...
Random Noise and Pole-Dynamics in Unstable Front Propagation II
Random Noise Pole-Dynamics Propagation analytic tool
2011/7/5
The current paper is a corrected version of our previous paper [1]. Similarly to previous version
we investigate the problem of flame propagation. This problem is studied as an example of unstable
f...
Bounds on the suprema of Gaussian processes, and omega results for the sum of a random multiplicative function
suprema of Gaussian processes omega results random multiplicative function
2011/1/17
We prove new lower bounds for the upper tail probabilities of suprema of Gaussian processes. Unlike many existing bounds, our results are not asymptotic,but supply strong information when one is only ...
Random multiplicative functions in short intervals
Random multiplicative functions short intervals
2010/11/24
We consider random multiplicative functions taking the values $\pm 1$. Using Stein's method for normal approximation, we prove a central limit theorem for the sum of such multiplicative functions in a...
On correlation function of high moments of Wigner random matrices
correlation function Wigner random matrices
2010/11/23
We consider the Wigner ensemble of Hermitian n-dimensional random matrices and study the correlation function K(s',s") of their moments in the limit when the numbers s', s" of the moments are proporti...
Concave Majorants of Random Walks and Related Poisson Processes
Concave Majorants Related Poisson Processes
2010/11/19
We offer a unified approach to the theory of concave majorants of random walks by providing a path transformation for a walk of finite length that leaves the law of the walk unchanged whilst providin...
Asymptotic of geometrical navigation on a random set of points of the plane
Asymptotic of geometrical navigation random set of points plane
2010/12/10
A navigation on a set of points is a rule for choosing which point to move to from the
present point in order to progress toward a specified target. In the present paper we study
some “geometrical b...
Quantum invariants of random 3-manifolds
quantum invariants random 3-manifolds Heegaard genus
2010/12/1
We consider the SO(3) Witten-Reshetikhin-Turaev quantum invariants
of random 3-manifolds. When the level r is prime, we show that the asymptotic distribution of the absolute value of these invariants...
The Distribution of Unbounded Random Sets and the Multivalued Strong Law of Large Numbers in Nonreflexive Banach Spaces
distribution of random sets multivalued strong law of large numbers set convergence measurable multifunctions convex sets
2009/1/20
In the first part, we introduce appropriate tools concerning the distribution of random sets. We study the relation between the distribution of a random set, whose values are closed subsets of a Banac...
Inequalities on the Variances of Convex Functions of Random Variables
Convex functions variance
2010/1/22
We develop inequalities relating to the variances of convex decreasing functions of random variables using information on the functions and the distribution functions of the random variables.
Inequalities of Maximum of Partial Sums and Weak Convergence for a Class Weak Dependent Random Variables
$\rho^{-}$-mixing $\rho^{*}$-mixing NA rosenthal type inequalities weak convergence
2007/12/12
In this paper, we establish a Rosenthal-type inequality of the maximum of partial sums for $\rho^{-}$-mixing random fields. As its applications we get the H\'{a}jeck--R\`{e}nyi inequality and weak con...
On the Distribution of Random Dirichlet Series in the Whole Plane
Random Dirichlet series Order(R) strong Borel line little function
2010/2/25
For some random Dirichlet series of order(R) infinite almost surely, every horizontal line is a strong Borel line of order(R) infinite and without exceptional Little functions.