Related papers: Operator-valued spectral measures and large deviat…
Spectral functions of symmetric matrices -- those depending on matrices only through their eigenvalues -- appear often in optimization. A cornerstone variational analytic tool for studying such functions is a formula relating their…
The theory of large deviations is concerned with the exponential decay of probabilities of large fluctuations in random systems. These probabilities are important in many fields of study, including statistics, finance, and engineering, as…
We study the operator associated to a random walk on $\R^d$ endowed with a probability measure. We give a precise description of the spectrum of the operator near $1$ and use it to estimate the total variation distance between the iterated…
We study the asymptotic behavior of the appropriately scaled and possibly perturbed spectral measure $\mu$ of large random real symmetric matrices with heavy tailed entries. Specifically, consider the N by N symmetric matrix $Y_N^\sigma$…
Invariant functions and metrics are studied on various classes of domains in $\Bbb C^n.$
We analyze the spectral properties of large, time-lagged correlation matrices using the tools of random matrix theory. We compare predictions of the one-dimensional spectra, based on approaches already proposed in the literature. Employing…
We analyze the extreme value dependence of independent, not necessarily identically distributed multivariate regularly varying random vectors. More specifically, we propose estimators of the spectral measure locally at some time point and…
We study refinements between spectral resolutions in an arbitrary II$_1$ factor $\M$ and obtain diffuse (maximal) refinements of spectral resolutions. We construct models of operators with respect to diffuse spectral resolutions. As an…
We present several natural notions of distance between spectral density functions of (discrete-time) random processes. They are motivated by certain filtering problems. First we quantify the degradation of performance of a predictor which…
We introduce the class of weighted "rotation-like" operators and study general properties of essential spectra of such operators. Then we use this approach to investigate and in some cases completely describe essential spectra of weighted…
In this paper we construct general vector-valued infinite-divisible independently scattered random measures with values in $\mathbb{R}^m$ and their corresponding stochastic integrals. Moreover, given such a random measure, the class of all…
Spectral measures arise in numerous applications such as quantum mechanics, signal processing, resonances, and fluid stability. Similarly, spectral decompositions (pure point, absolutely continuous and singular continuous) often…
Inverse spectral problems are studied for the second order integro-differential operators on a finite interval. Properties of spectral characteristic are established, and the uniqueness theorem is proved for this class of inverse problems.
Dynamical spectral estimation is a well-established numerical approach for estimating eigenvalues and eigenfunctions of the Markov transition operator from trajectory data. Although the approach has been widely applied in biomolecular…
We study large deviation properties of Telecom processes appearing as limits in a critical regime of infinite source Poisson models.
We consider a multinomial distribution, where the number of cells increases and the cell-probabilities decreases as the number of observations grows. The probabilities of large deviations of statistics, which has form of a sum of Borel…
We study the statistical convergence of metric valued sequences and of their subsequences. The interplay between the statistical and usual convergences in metric spaces is also studied.
Multivariate random fields whose distributions are invariant under operator-scalings in both time-domain and state space are studied. Such random fields are called operator-self-similar random fields and their scaling operators are…
The article is devoted to stochastic processes with values in finite- and infinite-dimensional vector spaces over infinite fields $\bf K$ of zero characteristics with non-trivial non-archimedean norms. For different types of stochastic…
We consider a "convolution mm-Laplacian" operator on metric-measure spaces and study its spectral properties. The definition is based on averaging over small metric balls. For reasonably nice metric-measure spaces we prove stability of…