Related papers: Furstenberg set problem and exceptional set estima…
The Lindblad equation for a two-level system under an electric field is analyzed by mapping to a linear equation with a non-Hermitian matrix. Exceptional points of the matrix are found to be extensive; the second-order ones are located on…
We consider the mean field theory of the Random Field Ising Model obtained by weighing the many solutions of the mean field equations with Boltzmann-like factors. These solutions are found numerically in three dimensions and we observe…
We resolve the function field analogue of the conjecture concerning distribution of twin primes in arithmetic progression.
We prove structural results for measure preserving systems, called Furstenberg systems, naturally associated with bounded multiplicative functions. We show that for all pretentious multiplicative functions these systems always have rational…
We prove both necessary and sufficient second order conditions of extrema for variational problems involving any higher order continuously twice differentiable Lagrangians with multi-valued dependent functions of several variables. Our…
In this work, new finite difference schemes are presented for dealing with the upper-convected time derivative in the context of the generalized Lie derivative. The upper-convected time derivative, which is usually encountered in the…
The most general form of a marginal extended perturbation in a two-dimensional system is deduced from scaling considerations. It includes as particular cases extended perturbations decaying either from a surface, a line or a point for which…
We are going to use the nickname "Das Budapester Programm" for a large class of finite combinatorial problems to be posed below. Following Klein's original idea, they concern various dimensional Euclidean spaces and several groups of…
Fix a point in a finite-dimensional complex vector space and consider the sequence of iterates of this point under the composition of a unitary map with the orthogonal projection on the hyperplane orthogonal to the starting point. We prove…
Assuming strong irreducibility and proximality, we prove that the Furstenberg measure, corresponding to a finitely supported measure on the general linear group of a finite dimensional real vector space, is exact dimensional. We also…
We investigate variants of Marstrand's projection theorem that hold for sets of directions and classes of sets in $\mathbb{R}^2$. We say that a set of directions $D \subseteq\mathcal{S}^1$ is $\textit{universal}$ for a class of sets if, for…
Max-stable random fields play a central role in modeling extreme value phenomena. We obtain an explicit formula for the conditional probability in general max-linear models, which include a large class of max-stable random fields. As a…
Motivated by recent results on radial projections and applications to the celebrated Falconer distance problem, we study radial projections in the setting of finite fields. More precisely, we extend results due to Mattila and Orponen…
The paper considers the problem of estimating a $p\geq2$\ dimensional mean vector of a multivariate conditionally normal distribution under quadratic loss. The problem of this type arises when estimating the parameters in a continuous time…
In this note we will describe a simple and practical approach to get rigorous bounds on the Hausdorff dimension of limits sets for some one dimensional Markov iterated function schemes. The general problem has attracted considerable…
In this paper, we study a second order variational problem for locally convex hypersurfaces, which is the affine invariant analogue of the classical Plateau problem for minimal surfaces. We prove existence, regularity and uniqueness results…
We introduce a framework for the design of finite element methods for two-dimensional moving boundary problems with prescribed boundary evolution that have arbitrarily high order of accuracy, both in space and in time. At the core of our…
Max-stable processes are increasingly widely used for modelling complex extreme events, but existing fitting methods are computationally demanding, limiting applications to a few dozen variables. $r$-Pareto processes are mathematically…
In this article, we develop a technique to "split" certain types of partially ordered sets into simpler ones and use that technique to give a partial answer to a conjecture by R. Wiegand and S. Wiegand on the structure of semi-local,…
We introduce a new class of singular partial differential equations, referred to as the second-order hyperbolic Fuchsian systems, and we investigate the associated initial value problem when data are imposed on the singularity. First, we…