Related papers: Limit theorems for record indicators in threshold …
In this paper we show that the limiting distribution of the real and the imaginary part of the double Fourier transform of a stationary random field is almost surely an independent vector with Gaussian marginal distributions, whose variance…
In this article, local limit theorems for sequences of simple random walks on graphs are established. The results formulated are motivated by a variety of random graph models, and explanations are provided as to how they apply to…
Control charts for process monitoring are widely used in practice. Most control charts require the monitored (residuals) process to be serially independent (and to satisfy specified distributional assumptions), whereas undetected dependence…
In this paper, we construct a moment inequality for mixing dependent random variables, it is of independent interest. As applications, the consistency of the kernel density estimation is investigated. Several limit theorems are established:…
Donsker-type functional limit theorems are proved for empirical processes arising from discretely sampled increments of a univariate L\'evy process. In the asymptotic regime the sampling frequencies increase to infinity and the limiting…
Consider the normalized partial sums of a real-valued function $F$ of a Markov chain, \[\phi_n:=n^{-1}\sum_{k=0}^{n-1}F(\Phi(k)),\qquad n\ge1.\] The chain $\{\Phi(k):k\ge0\}$ takes values in a general state space $\mathsf {X}$, with…
Conditional independence and Markov properties are powerful tools allowing expression of multidimensional probability distributions by means of low-dimensional ones. As multidimensional possibilistic models have been studied for several…
We present a general methodology to construct triplewise independent sequences of random variables having a common but arbitrary marginal distribution $F$ (satisfying very mild conditions). For two specific sequences, we obtain in closed…
The $\alpha$-stable distributions introduced by L\'evy play an important role in probabilistic theoretical studies and their various applications, e.g., in statistical physics, life sciences, and economics. In the present paper we study…
It is known that first-order logic with some counting extensions can be efficiently evaluated on graph classes with bounded expansion, where depth-$r$ minors have constant density. More precisely, the formulas are $\exists x_1 ... x_k \#y…
We consider a non-nestling random walk in a product random environment. We assume an exponential moment for the step of the walk, uniformly in the environment. We prove an invariance principle (functional central limit theorem) under almost…
Finsler's lemma is a classic mathematical result with applications in control and optimization. When the lemma is applied to parameter-dependent LMIs, as such those that arise from problems of robust stability, the extra variables…
We consider the Fleming--Viot particle system associated with a continuous-time Markov chain in a finite space. Assuming irreducibility, it is known that the particle system possesses a unique stationary distribution, under which its…
Counting independent sets in graphs and hypergraphs under a variety of restrictions is a classical question with a long history. It is the subject of the celebrated container method which found numerous spectacular applications over the…
The fluctuation theorem for entropy production is a remarkable symmetry of the distribution of produced entropy that holds universally in non-equilibrium steady states with Markovian dynamics. However, in systems with slow degrees of…
The Central Limit Theorem provides a foundation for inferential statistics and hypothesis testing. It describes how standardized statistics behave under repeated sampling from large populations. However, if the size of the sample (n)…
We consider Ewens random permutations of length $n$ conditioned to have no cycle longer than $n^\beta$ with $0<\beta<1$ and to study the asymptotic behaviour as $n\to\infty$. We obtain very precise information on the joint distribution of…
Our goal is to develop theory and algorithms for establishing fundamental limits on performance imposed by a robot's sensors for a given task. In order to achieve this, we define a quantity that captures the amount of task-relevant…
Random spatial networks-that is, graphs whose connectivity is governed by geometric proximity-have emerged as fundamental models for systems constrained by an underlying spatial structure. A prototypical example is the random geometric…
We study statistics of records in a sequence of random variables. These identical and independently distributed variables are drawn from the parent distribution rho. The running record equals the maximum of all elements in the sequence up…