Related papers: The G\"{a}rtner-Ellis theorem, homogenization, and…
This article includes a short survey of selected averaging and dimension reduction techniques for deterministic fast-slow systems. This survey includes, among others, classical techniques, such as the WKB approximation or the averaging…
We consider the variant of stochastic homogenization theory introduced in [X. Blanc, C. Le Bris and P.-L. Lions, C. R. Acad. Sci. Serie I 2006 and Journal de Mathematiques Pures et Appliquees 2007]. The equation under consideration is a…
We derive a large deviation principle for families of random variables in the basin of attraction of spectrally positive stable distributions by proving a uniform version of the Tauberian theorem for Laplace-Stieltjes transforms. The main…
This work has been motivated by recent papers that quantify the density of values of generic quadratic forms and other polynomials at integer points, in particular ones that use Rogers' second moment estimates. In this paper we establish…
This paper studies a class of exponential family models whose canonical parameters are specified as linear functionals of an unknown infinite-dimensional slope function. The optimal minimax rates of convergence for slope function estimation…
The theory of uniform approximation of real numbers motivates the study of products of consecutive partial quotients in regular continued fractions. For any non-decreasing positive function $\varphi:\mathbb{N}\to [2,\infty)$, we determine…
The large deviation principle in the small noise limit is derived for solutions of possibly degenerate It\^o stochastic differential equations with predictable coefficients, which may depend also on the large deviation parameter. The result…
The subject of this work is an adaptive stochastic Galerkin finite element method for parametric or random elliptic partial differential equations, which generates sparse product polynomial expansions with respect to the parametric…
This work is concerned with the rigorous analysis on the Generalized Multiscale Finite Element Methods (GMsFEMs) for elliptic problems with high-contrast heterogeneous coefficients. GMsFEMs are popular numerical methods for solving flow…
We prove that for a finite collection of real-valued functions $f_{1},...,f_{n}$ on the group of complex numbers of modulus 1 which are derivable with Lipschitz continuous derivative, the distribution of $(\tr f_{1},...,\tr f_{n})$ under…
The metrical theory of the product of consecutive partial quotients is associated with the uniform Diophantine approximation, specifically to the improvements to Dirichlet's theorem. Achieving some variant forms of metrical theory in…
In this paper we consider the growth, large fluctuations and memory properties of an affine stochastic functional differential equation with an average functional where the contributions of the average and instantaneous terms are…
The Hirschfeld-Gebelein-R\'{e}nyi (HGR) maximal correlation and the corresponding functions have been shown useful in many machine learning scenarios. In this paper, we study the sample complexity of estimating the HGR maximal correlation…
In this paper we establish new integral representations for the remainder term of the known asymptotic expansion of the logarithm of the Barnes $G$-function. Using these representations, we obtain explicit and numerically computable error…
We investigate the behavior of the rare fluctuations of the free energy in the p-spin spherical model, evaluating the corresponding rate function via the G\"artner-Ellis theorem. This approach requires the knowledge of the analytic…
Starting from the equation obeyed by the derivative, we construct several expansions of the solutions of the general Heun equation in terms of the Appell generalized hypergeometric functions of two variables of the fist kind. Several cases…
We consider Jack measures on partitions with homogeneous defining specializations. For each of the six distinct classes of measures obtained this way we prove a global law of large numbers with an explicit limiting particle density. We also…
We present a second-order extension of the first-order Lohe hermitian sphere(LHS) model and study its emergent asymptotic dynamics. Our proposed model incorporates an inertial effect as a second-order extension. The inertia term can…
The flux reconstruction (FR) approach offers a flexible framework for describing a range of high-order numerical schemes; including nodal discontinuous Galerkin and spectral difference schemes. This is accomplished through the use of…
The goal of this expository article is a fairly self-contained account of some averaging processes of functions along sequences of the form $(\alpha^n x)^{}_{n\in\mathbb{N}}$, where $\alpha$ is a fixed real number with $| \alpha | > 1$ and…