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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 ...
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 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...
.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...
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...
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 ...
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...
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...
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...
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...
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...
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...
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.
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...
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.

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