Related papers: Limit theorems for $p$-domain functionals of stati…

In this paper, we use crossing symmetry and unitarity constraints to put a lower bound on the central charge of conformal field theories in large space-time dimensions $D$. Specifically, we work with the four-point function of identical…

Stochastic dynamical systems consisting of non-invertible continuous maps on an interval are studied. It is proved that if they satisfy the recently introduced so-called $\mu$-injectivity and some mild assumptions, then proximality,…

In this paper, concerning SDEs with H\"older continuous drifts, which are merely dissipative at infinity, and SDEs with piecewise continuous drifts, we investigate the strong law of large numbers and the central limit theorem for underlying…

We extend the central limit theorem under the Dedecker-Rio condition to adapted stationary and ergodic sequences of random variables taking values in a class of smooth Banach spaces. This result applies to the case of random variables…

A strengthened version of the central limit theorem for discrete random variables is established, relying only on information-theoretic tools and elementary arguments. It is shown that the relative entropy between the standardised sum of…

We study a class of discrete-time random walks in $\mathbb{R}^d$ whose conditional drift decays polynomially in time and grows polynomially with the distance from the origin to the current position. This class is related to several models…

This paper studies the behavior of the entropy numbers of classes of functions with bounded integral norms from a given finite dimensional linear subspace. Upper bounds of these entropy numbers in the uniform norm are obtained and applied…

Let $\{X(\mathbf{t}):\mathbf{t}=(t_1, t_2, \ldots, t_d)\in[0,\infty)^d\}$ be a centered stationary Gaussian field with almost surely continuous sample paths, unit variance and correlation function $r$ satisfying conditions $r(\mathbf{t})<1$…

In this article we generalize the classical Edgeworth expansion for the probability density function (PDF) of sums of a finite number of symmetric independent identically distributed random variables with a finite variance to sums of…

For $ p \in (1,N)$ and a domain $\Omega$ in $\mathbb{R}^N$, we study the following quasi-linear problem involving the critical growth: \begin{eqnarray*} -\Delta_p u - \mu g|u|^{p-2}u = |u|^{p^{*}-2}u \ \mbox{ in } \mathcal{D}_p(\Omega),…

We consider a class of Gibbs measures defined with respect to increments $\{\omega(t)-\omega(s)\}_{s<t}$ of $d$-dimensional Wiener measure, with the underlying Hamiltonian carrying interactions of the form $H(t-s,\omega(t)-\omega(s))$ that…

We start by revisiting the derivation of the variational formulae for the functional assigning to a bounded regular domain in a Riemannian manifold its first Dirichlet eigenvalue and extend it to (not necessarily bounded) domains in certain…

We consider a positive recurrent one-dimensional diffusion process with continuous coefficients and we establish stable central limit theorems for a certain type of additive functionals of this diffusion. In other words we find some…

We consider the Cauchy-Dirichlet problem to systems with $p$-growth structure with $1 < p < \infty$, whose prototype is \begin{equation*} \partial_t u- \operatorname{div} \big( |Du|^{p-2} Du \big) = \operatorname{div} \left( |F|^{p-2} F…

We obtain an elementary invariance principle for multi-dimensional Brownian sheet where the underlying random fields are not necessarily independent or stationary. Possible applications include unit-root tests for spatial as well as panel…

Let $(X_{k})_{k \in \mathbb Z }$ be a linear process with values in a separable Hilbert space $\mathbb{H}$ given by $X_{k} =\sum_{j=0}^{\infty} (j+1)^{-N}\varepsilon_{k-j}$ for each $k \in \mathbb Z$, where $N:\mathbb{H} \to \mathbb{H}$ is…

We show a new functional limit theorem for weakly dependent regularly varying sequences of random vectors. As it turns out, the convergence takes place in the space of R^d valued c\`{a}dl\`{a}g functions endowed with the so-called weak M1…

With the help of a radially invariant vector field, we derive inequalities of the Hardy kind, with no boundary terms, for $W^{1,p}$ functions on bounded star domains. Our results are not obtainable from the classical inequalities for…

We present normal approximation results at the process level for local functionals defined on dynamic Poisson processes in $\mathbb{R}^d$. The dynamics we study here are those of a Markov birth-death process. We prove functional limit…

For a stationary sequence of random variables we derive a self-normalized functional limit theorem under joint regular variation with index $\alpha \in (0,2)$ and weak dependence conditions. The convergence takes place in the space of…