1. Some aspects of classical empirical process theory: uniform laws of large numbers, process convergence and uniform central limit theorems. 2. M-estimation. Asymptotic theory of consistency, rates of convergence and limiting distribution. 3. Non-asymptotic theory of penalized empirical risk minimization; nonasymptotic deviation inequalities for suprema of empirical processes, oracle inequalit...

In this paper we study the property of asymptotic completeness in (massive) Euclidean lattice quantum field theories. We use the methods of Spencer and Zirilli [2] to prove, under suitable hypothesis, two-body asymptotic completeness, i.e., for the energy range just above the two-particle threshold.

The asymptotic lattices and their transformations are studied within the line geometry approach. It is shown that the discrete asymptotic nets are represented by isotropic congruences in the Plücker quadric. On the basis of the Lelieuvre-type representation of asymptotic lattices and of the discrete analog of the Moutard transformation, it is constructed the discrete analog of the W–congruences...

We define a type of generalized asymptotic series called v-asymptotic. We show that every function with moderate growth at infinity has a v-asymptotic expansion. We also describe the set of v-asymptotic series, where a given function with moderate growth has a unique v-asymptotic expansion. As an application to random matrix theory we calculate the coefficients and establish the uniqueness of t...

The Casimir attraction can significantly interfere the physical response of nanoactuators. The intensity of the Casimir force depends on the geometries of interacting bodies. The present paper is dedicated to model the influence of the Casimir attraction on the electrostatic stability of nanoactuators made of cylindrical conductive nanowire/nanotube. An asymptotic solution, based on path-integr...

In this paper, global robust stability of stochastic impulsive recurrent neural networks with time-varyingdelays which are represented by the Takagi-Sugeno (T-S) fuzzy models is considered. A novel Linear Matrix Inequality (LMI)-based stability criterion is obtained by using Lyapunov functional theory to guarantee the asymptotic stability of uncertain fuzzy stochastic impulsive recurrent neural...

Asymptotic states in field theories containing non-local kinetic terms are analyzed using the canonical method, naturally defined in Minkowski space. We apply our results to study the asymptotic states of a non-local MaxwellChern-Simons theory coming from bosonization in 2+1 dimensions. We show that in this case the only asymptotic state of the theory, in the trivial (nontopological) sector, is...

We are concerned with asymptotic analysis for linear difference equations in a locally convex space. First we introduce the profile operator, which plays a central role in analyzing the asymptotic behaviors of the solutions. Then factorial asymptotic expansions for the solutions are given quite explicitly. Finally we obtain Gevrey estimates for the solutions. In a forthcoming paper we will deve...