Related papers: Sanov-type large deviations and conditional limit …
In this paper, we provide a unifying theory concerning the convergence properties of the so-called max-product Kantorovich sampling operators based upon generalized kernels in the setting of Orlicz spaces. The approximation of functions…
The classical Dvoretzky--Rogers lemma provides a deterministic algorithm by which, from any set of isotropic vectors in Euclidean $d$-space, one can select a subset of $d$ vectors whose determinant is not too small. Subsequently,…
The asymptotic analysis of a class of stochastic partial differential equations (SPDEs) with fully locally monotone coefficients covering a large variety of physical systems, a wide class of quasilinear SPDEs and a good number of fluid…
We investigate three types of averaging principles and the normal deviation for multi-scale stochastic differential equations (in short, SDEs) with polynomial nonlinearity. More specifically, we first demonstrate the strong convergence of…
We consider a random geometric graph $G(\chi_n, r_n)$, given by connecting two vertices of a Poisson point process $\chi_n$ of intensity $n$ on the unit torus whenever their distance is smaller than the parameter $r_n$. The model is…
We consider a stochastic 2D Navier-Stokes equation in a bounded domain. The random force is assumed to be non-degenerate and periodic in time, its law has a support localised with respect to both time and space. Slightly strengthening the…
Let $r=r(n)$ be a sequence of integers such that $r\leq n$ and let $X_1,\ldots,X_{r+1}$ be independent random points distributed according to the Gaussian, the Beta or the spherical distribution on $\mathbb{R}^n$. Limit theorems for the…
We are dealing with the validity of a large deviation principle for a class of reaction-diffusion equations with polynomial nonlinearity, perturbed by a Gaussian random forcing. We are here interested in the regime where both the strength…
An extension of Marcinkiewicz Interpolation Theorem, allowing intermediate spaces of Orlicz type, is proved. This generalization yields a necessary and sufficient condition so that every quasilinear operator, which maps the set, $S(X,\mu)$,…
We give some natural sufficient conditions for balls in a metric space to have small intersection. Roughly speaking, this happens when the metric space is (i) expanding and (ii) well-spread, and (iii) a certain random variable on the…
In this paper, we considier the limiting distribution of the maximum interpoint Euclidean distance $M_n=\max _{1 \leq i<j \leq n}\left\|\boldsymbol{X}_i-\boldsymbol{X}_j\right\|$, where $\boldsymbol{X}_1, \boldsymbol{X}_2, \ldots,…
We present large deviations estimates in the supremum norm for a system of independent random walks superposed with a birth-and-death dynamics evolving on the discrete torus with $N$ sites. The scaling limit considered is the so-called…
We derive the limit null distribution of the class of Sobolev tests of uniformity on the hypersphere when the dimension and the sample size diverge to infinity at arbitrary rates. The limiting non-null behavior of these tests is obtained…
Let $(Z_{n})$ be a supercritical branching process in a random environment $\xi $, and $W$ be the limit of the normalized population size $Z_{n}/\mathbb{E}[Z_{n}|\xi ]$. We show large and moderate deviation principles for the sequence $\log…
We describe a very general abstract form of sieve based on a large sieve inequality which generalizes both the classical sieve inequality of Montgomery (and its higher-dimensional variants), and our recent sieve for Frobenius over function…
In this article we establish a large deviation principle for the family {\nu_{\epsilon}:\epsilon \in (0,1)} of distributions of the scaled stochastic processes {P_{-\log\sqrt{\epsilon}}Z_t}_{t\leq 1}, where (Z_t)_{t\in \lbrack 0,1]} is a…
Based on a novel type of Sobolev-Poincar\'e inequality (for generalised weakly differentiable functions on varifolds), we establish a finite upper bound of the geodesic diameter of generalised compact connected surfaces-with-boundary of…
In this work, an analytical Volume Of Fluid (VOF) implementation of the Generalized Navier Boundary Condition is presented based on the Brackbill surface tension model. The model is validated by simulations of droplets on a smooth surface…
In this paper, we show the existence of non-trivial solutions to very general elliptic systems with critical non-linearities in the sense of embeddings in Orlicz-Sobolev spaces. This allows to consider non-linearities which do not have…
We present a large deviation principle at speed N for the largest eigenvalue of some additively deformed Wigner matrices. In particular this includes Gaussian ensembles with full-rank general deformation. For the non-Gaussian ensembles, the…