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During the last years, asymptotic (or sequential) constraint qualifications, which postulate upper semicontinuity of certain set-valued mappings and provide a natural companion of asymptotic stationarity conditions, have been shown to be…
In this paper we study the asymptotic behaviour of weighted random sums when the sum process converges stably in law to a Brownian motion and the weight process has continuous trajectories, more regular than that of a Brownian motion. We…
In this article we prove existence of the asymptotic capacity of the range of random walks on free products of graphs. In particular, we will show that the asymptotic capacity of the range is almost surely constant and strictly positive.…
The aim of this article is to establish asymptotic distributions and consistency of subsampling for spectral density and for magnitude of coherence for non-stationary, almost periodically correlated time series. We show the asymptotic…
We define correlational (von Neumann) entropy for an individual quantum state of a system whose time-independent hamiltonian contains random parameters and is treated as a member of a statistical ensemble. This entropy is representation…
The asymptotic behavior of stochastic gradient algorithms is studied. Relying on results from differential geometry (Lojasiewicz gradient inequality), the single limit-point convergence of the algorithm iterates is demonstrated and…
We derive theorems which outline explicit mechanisms by which anomalous scaling for the probability density function of the sum of many correlated random variables asymptotically prevails. The results characterize general anomalous scaling…
We propose a form factor approach for the computation of the large distance asymptotic behavior of correlation functions in quantum critical (integrable) models. In the large distance regime we reduce the summation over all excited states…
We study the asymptotic behavior, as time t goes to infinity, of nonautonomous dynamical systems involving multiscale features. These systems model the emergence of various collective behaviors in game theory, as well as the asymptotic…
For a set of dependent random variables, without stationary or the strong mixing assumptions, we derive the asymptotic independence between their sums and maxima. Then we apply this result to high-dimensional testing problems, where we…
Accurate quantification of model uncertainty has long been recognized as a fundamental requirement for trusted AI. In regression tasks, uncertainty is typically quantified using prediction intervals calibrated to a specific operating point,…
We introduce a novel notion of invariance feedback entropy to quantify the state information that is required by any controller that enforces a given subset of the state space to be invariant. We establish a number of elementary properties,…
Critical intermittency stands for a type of intermittent dynamics in iterated function systems, caused by an interplay of a superstable fixed point and a repelling fixed point. We consider critical intermittency for iterated function…
This paper proposes parametric and non-parametric hypothesis testing algorithms for detecting anisotropy -- rotational variance of the covariance function in random fields. Both algorithms are based on resampling mechanisms, which enable…
We consider high-dimensional estimation problems where the number of parameters diverges with the sample size. General conditions are established for consistency, uniqueness, and asymptotic normality in both unpenalized and penalized…
We propose a nonparametric procedure to test for changes in correlation matrices at an unknown point in time. The new test requires only mild assumptions on the serial dependence structure and has considerable power in finite samples. We…
We introduce a new approach to the the asymptotic iteration method (AIM) by means of which we establish the standard AIM connection with the continued fractions technique and we develop a novel termination condition in terms of the…
For a family of random intermittent dynamical systems with a superattracting fixed point we prove that a phase transition occurs between the existence of an absolutely continuous invariant probability measure and infinite measure depending…
General Central limit theorem deals with weak limits (in type) of sums of row-elements of array random variables. In some situations as in the invariance principle problem, the sums may include only parts of the row-elements. For strictly…
The talk presented at ICMP 97 focused on the scaling limits of critical percolation models, and some other systems whose salient features can be described by collections of random lines. In the scaling limit we keep track of features seen…