Related papers: A uniform stability principle for dual lattices

Let $\{V_{i,j}; (i,j)\in\N^2\}$ be a two-dimensional array of i.i.d.\ random variables. The limit laws of the sum of independent random products $$ Z_n=\sum_{i=1}^{N_n} \prod_{j=1}^{n} e^{V_{i,j}} $$ as $n,N_n\to\infty$ have been…

We define a natural notion of higher order stability and show that subsets of $\mathbb{F}_p^n$ that are tame in this sense can be approximately described by a union of low-complexity quadratic varieties, up to linear error. This generalizes…

This paper provides a comprehensive analysis of stability and long-time behaviour of a coupled system constituted by two rigid bodies separated by a thin layer of lubricant. We show that permanent rotations of the whole system, with the…

In the present paper we obtain a new correlation inequality and use it for the purpose of extending the theory of the Almost Sure Local Limit Theorem to the case of lattice random sequences in the domain of attraction of a stable law. In…

We prove that for any integral lattice $\mathcal{L} \subset \mathbb{R}^n$ (that is, a lattice $\mathcal{L}$ such that the inner product $\langle \mathbf{y}_1,\mathbf{y}_2 \rangle$ is an integer for all $\mathbf{y}_1, \mathbf{y}_2 \in…

The discrepancy of a point set quantifies how well the points are distributed, with low-discrepancy point sets demonstrating exceptional uniform distribution properties. Such sets are integral to quasi-Monte Carlo methods, which approximate…

We define bidual bounded $uo$-convergence in vector lattices and investigate relations between this convergence and $b$-property. We prove that for a regular Riesz dual system $\langle X,X^{\sim}\rangle$, $X$ has $b$-property if and only if…

This work is devoted to the study of the nonlinear second-order neutral difference equations with quasi-differences of the form $$ \Delta \left( r_{n} \Delta \left( x_{n}+q_{n}x_{n-\tau}\right)\right)= a_{n}f(x_{n-\sigma})+b_n%, \ n\geq n_0…

We prove the asymptotic stability of the equilibrium solution of a class of vector Li\'enard equations by means of LaSalle invariance principle. The key hypothesis consists in assuming that the intersections of the manifolds in $\{\dot V =…

An important consequence of the Hahn-Banach Theorem says that on any locally convex Hausdorff topological space $X$, there are sufficiently many continuous linear functionals to separate points of $X$. In the paper, we establish a `local'…

Let $X $ be a square integrable random variable with basic probability space $(\O, \A, \P)$, taking values in a lattice $\mathcal L(v_0,1)=\big\{v_k=v_0+ k,k\in \Z\big\}$ and such that $\t_X =\sum_{k\in \Z}\P\{X=v_k\}\wedge…

Let $ l =[l_0,l_1]$ be the directed line segment from $l_0\in {\mathbb R}^n$ to $l_1\in{\mathbb R}^n.$ Suppose $\bar l=[\bar l_0,\bar l_1]$ is a second segment of equal length such that $l, \bar l$ satisfy the "two sticks condition": $\|…

The main aim of the present note is to consider bounded orthomorphisms between locally solid vector lattices. We establish a version of the remarkable Zannen theorem regarding equivalence between orthomomorphisms and the underlying vector…

We show for several two-dimensional lattices that the nearest neighbor valence bond states are linearly independent. To do so, we utilize and generalize a method that was recently introduced and applied to the kagome lattice by one of the…

Percolation theory is usually applied to lattices with a uniform probability p that a site is occupied or that a bond is closed. The more general case, where p is a function of the position x, has received less attention. Previous studies…

This paper investigates the construction of space-filling designs for computer experiments. The space-filling property is characterized by the covering and separation radii of a design, which are integrated through the unified criterion of…

We ask whether a stationary lattice in dimension $d$ whose points are shifted by identically distributed but possibly dependent perturbations remains hyperuniform. When $d = 1$ or $2$, we show that it is the case when the perturbations have…

This paper is concerned with a relative uniform Yau--Tian--Donaldson correspondence, in terms of test configurations, for the projectivization \( \mathbb{P}(E) \) of a holomorphic vector bundle \( E \) over a smooth curve. For any K\"ahler…

The consistency problem for a class of algebraic structures asks for an algorithm to decide for any given conjunction of equations whether it admits a non-trivial satisfying assignment within some member of the class. By Adyan (1955) and…

This article develops a moderate-deviation limit theory for autoregressive models with jointly persistent mean and volatility dynamics. The autoregressive coefficient is allowed to drift toward unity slower than the classical 1/n rate,…