Related papers: Limit theorems for filtered long-range dependent r…
Structural properties of large random maps and lambda-terms may be gleaned by studying the limit distributions of various parameters of interest. In our work we focus on restricted classes of maps and their counterparts in the…
The standard central limit theorem with a Gaussian attractor for the sum of independent random variables may lose its validity in presence of strong correlations between the added random contributions. Here, we study this problem for…
We consider "randomized" statistics constructed by using a finite number of observations a random field at randomly chosen points. We generalize the invariance principle (the functional CLT), the Glivenko--Cantelli theorem, the theorem…
Regression models for limited continuous dependent variables having a non-negligible probability of attaining exactly their limits are presented. The models differ in the number of parameters and in their flexibility. Fractional data being…
The spatial distribution of galaxies is a highly complex phenomenon currently impossible to predict deterministically. However, by using a statistical $\textit{bias}$ relation, it becomes possible to robustly model the average abundance of…
We consider random rectangles in $\mathbb{R}^2$ that are distributed according to a Poisson random measure, i.e., independently and uniformly scattered in the plane. The distributions of the length and the width of the rectangles are…
This paper studies high-order partial differential equations with random initial conditions that have both long-memory and cyclic behavior. The cases of random initial conditions with the spectral singularities, both at zero (representing…
This paper investigates the approximation of Gaussian random variables in Banach spaces, focusing on the high-probability bounds for the approximation of Gaussian random variables using finitely many observations. We derive non-asymptotic…
The analysis of spatial extremes requires the joint modeling of a spatial process at a large number of stations and max-stable processes have been developed as a class of stochastic processes suitable for studying spatial extremes. Spatial…
Second-order characteristics including covariance and spectral density functions are fundamentally important for both statistical applications and theoretical analysis in functional time series. In the high-dimensional setting where the…
We develop a multi-level restricted Gaussian maximum likelihood method for estimating the covariance function parameters and computing the best unbiased predictor. Our approach produces a new set of multi-level contrasts where the…
We provide theoretical procedures and practical recipes to simulate non-Gaussian correlated, homogeneous random fields with prescribed marginal distributions and cross-correlation structure, either in a N-dimensional Cartesian space or on…
We introduce Gaussian orthogonal latent factor processes for modeling and predicting large correlated data. To handle the computational challenge, we first decompose the likelihood function of the Gaussian random field with a…
We generalize the diffusion-limited aggregation by issuing many randomly-walking particles, which stick to a cluster at the discrete time unit providing its growth. Using simple combinatorial arguments we determine probabilities of…
In this paper, we characterize the convergence of the (rescaled logarithmic) empirical spectral distribution of wavelet random matrices. We assume a moderately high-dimensional framework where the sample size $n$, the dimension $p(n)$ and,…
Recently, a generalized Bernoulli process (GBP) was developed as a stationary binary sequence that can have long-range dependence. In this paper, we find the scaling limit of a random walk that follows GBP. The result is a new class of…
In the paper we present simple examples of linear random fields defined on $\ZZ^2$ and $\ZZ^3$ which exhibit the scaling transition phenomenon. These examples lead to more general definition of the scaling transition and allow to understand…
This is an extended version of a series of talks I held at the University of Bochum in 2017 about limit theorems for non-linear functionals of stationary Gaussian random fields. The goal of these talks was to give a fairly detailed…
We study random Hamiltonians on finite-size cubes and waveguide segments of increasing diameter. The number of random parameters determining the operator is proportional to the volume of the cube. In the asymptotic regime where the cube…
We study non-linear additive functionals of stationary Gaussian fields over anisotropically growing domains in $\mathbb{R}^d$, including spatiotemporal settings, and establish Gaussian and non-Gaussian limit theorems under non-separable…