Related papers: A Local Limit Theorem for Linear Random Fields
Consider a sequence of independent random isometries of Euclidean space with a previously fixed probability law. Apply these isometries successively to the origin and consider the sequence of random points that we obtain this way. We prove…
Different extended objects can fall in different ways, depending on their internal structures. Some motions are nevertheless impossible, regardless of internal structure. This paper derives universal constraints on extended-body motion,…
In a previous article, we introduced a reduction procedure for locally conformally symplectic manifolds at any regular value of the momentum mapping. We use this construction to prove an analogue of a well-known theorem in the symplectic…
A linear recurrence sequence in a cyclotomic field produces a sequence of the generating fields of each term. We show that the later sequence is periodic after removing the first finite terms, and give a bound of its period. This can be…
We extend to any maximally entangled state of a bipartite system whose constituents are arbitrarily (but finite) dimensional the result, recently derived for two-dimensional constituents, that hidden variable theories cannot have local…
Under an appropriate regular variation condition, the affinely normalized partial sums of a sequence of independent and identically distributed random variables converges weakly to a non-Gaussian stable random variable. A functional version…
General Central limit theorem deals with weak limits (in type) of sums of row-elements of array random variables. In some situations as in the invariance principle problem, the sums may include only parts of the row-elements. For strictly…
We prove a sequence of limiting results about weakly dependent stationary and regularly varying stochastic processes in discrete time. After deducing the limiting distribution for individual clusters of extremes, we present a new type of…
The Central Limit Theorem states that, in the limit of a large number of terms, an appropriately scaled sum of independent random variables yields another random variable whose probability distribution tends to a stable distribution. The…
Let $X=\{X_n: n\in\mathbb{N}\}$ be a linear process in which the coefficients are of the form $a_i=i^{-1}\ell(i)$ with $\ell$ being a slowly varying function at the infinity and the innovations are independent and identically distributed…
The aim of the present work is to show that recent results of the authors on the approximation of distributions of sums of independent summands by the infinitely divisible laws on convex polyhedra can be shown via an alternative class of…
Numerous interesting properties in nonlinear systems analysis can be written as polynomial optimization problems with nonconvex sum-of-squares problems. To solve those problems efficiently, we propose a sequential approach of local…
In this paper some general theory is presented for locally stationary processes based on the stationary approximation and the stationary derivative. Laws of large numbers, central limit theorems as well as deterministic and stochastic bias…
We generalise the Erdos-Renyi limit theorem on the maximum of the partial sums of random variables to the case when the number of terms in these sums is randomly distributed. Certain relations between the limiting theorems of this type and…
We obtain new multilinear multiplier theorems for symbols of restricted smoothness which lie locally in certain Sobolev spaces. We provide applications concerning the boundedness of the commutators of Calder\'on and…
In this paper, we present the asymptotic theory for integrated functions of increments of Brownian local times in space. Specifically, we determine their first-order limit, along with the asymptotic distribution of the fluctuations. Our key…
We consider large random matrices $X$ with centered, independent entries which have comparable but not necessarily identical variances. Girko's circular law asserts that the spectrum is supported in a disk and in case of identical…
The Lov\'{a}sz Local Lemma is a very powerful tool in probabilistic combinatorics, that is often used to prove existence of combinatorial objects satisfying certain constraints. Moser and Tardos have shown that the LLL gives more than just…
This paper studies the limits of a spatial random field generated by uniformly scattered random sets, as the density $\lambda$ of the sets grows to infinity and the mean volume $\rho$ of the sets tends to zero. Assuming that the volume…
In this paper we consider uniformly random lozenge tilings of arbitrary domains approximating (after suitable normalization) a closed, simply-connected subset of $\mathbb{R}^2$ with piecewise smooth, simple boundary. We show that the local…