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We study the regularity of the distance function to the boundary of a domain in $\mathbb{R}^n$, with respect to the Minkowski functional of a convex polytope. We obtain the regularity of the distance function in certain cases. We also…
We study random dynamical systems of certain continuous functions on the unit interval. We use bounded variation to provide sufficient conditions for unique ergodicity of these systems. Several classes of examples are provided.
Matrix Dirichlet processes, in reference to their reversible measure, appear in a natural way in many different models in probability. Applying the language of diffusion operators and the method of boundary equations, we describe Dirichlet…
In this article we show how ideas, methods and results from optimal transportation can be used to study various aspects of the stationary measuresof Iterated Function Systems equipped with a probability distribution. We recover a classical…
A technique is introduced which allows to generate -- starting from any solvable discrete-time dynamical system involving N time-dependent variables -- new, generally nonlinear, generations of discrete-time dynamical systems, also involving…
We provide a sufficient condition for the bounded law of the iterated logarithms for strictly stationary random fields expressable as a functional of i.i.d. random fields when the summation is done on rectangles. The study is done via the…
We consider linear iterated function systems with a random multiplicative error on the real line. Our system is $\{x\mapsto d_i + \lambda_i Y x\}_{i=1}^m$, where $d_i\in \R$ and $\lambda_i>0$ are fixed and $Y> 0$ is a random variable with…
Generation of Wigner functions of Landau levels and determination of their symmetries and generic properties are achieved in the autonomous framework of deformation quantization. Transformation properties of diagonal Wigner functions under…
As an alternative to the well-known methods of "chaining" and "bracketing" that have been developed in the study of random fields, a new method, which is based on a stochastic maximal inequality derived by using the Taylor expansion, is…
We define a Wigner distribution function for a one-dimensional finite quantum system, in which the position and momentum operators have a finite (multiplicity-free) spectrum. The distribution function is thus defined on discrete…
The concept of boolean autonomous deterministic regular asynchronous system has its origin in switching theory, the theory of modeling the switching circuits from the digital electrical engineering. The attribute boolean vaguely refers to…
We consider iterated function systems (finite or countable), together with linear and continuous operators on Hilbert spaces, which enable us to construct Markov-type operators. Under suitable conditions, these Markov-type operators have…
We study random independent and identically distributed iterations of functions from an iterated function system of homeomorphisms on the circle which is minimal. We show how such systems can be analyzed in terms of iterated function…
This note aims to bring attention to a simple class of discrete dynamical systems exhibiting some complex behaviour. Each of these systems is defined as a self-mapping of the unit square and is obtained by coupling two families of…
We find all factorized duality functions for a class of interacting particle systems. The functions we recover are self-duality functions for interacting particle systems such as zero-range processes, symmetric inclusion and exclusion…
In this paper, we present methods of obtaining single moments of order statistics arising from posibly dependent and non-identically distributed discrete random variables. We derive exact and approximate formulas convenient for numerical…
In this paper, we establish a simple criterion for two $L$-functions $L_1$ and $L_2$ satisfying a functional equation (and some natural assumptions) to have infinitely many distinct zeros. Some related questions have already been answered…
The aim of this paper is to investigate discrete approximations of the exponential functional $\int_0^{\infty} \exp(B(t) - \nu t) \di t$ of Brownian motion (which plays an important role in Asian options of financial mathematics) by the…
We show that various functionals related to the supremum of a real function defined on an arbitrary set or a measure space are Hadamard directionally differentiable. We specifically consider the supremum norm, the supremum, the infimum, and…
Motivated by the normal form of a fast-slow ordinary differential equation exhibiting a pitchfork singularity we consider the discrete-time dynamical system that is obtained by an application of the explicit Euler method. Tracking…