Related papers: Ergodic Markov processes and Poisson equations (le…

This is a set of four lectures devoted to simple ideas about turbulent transport, a ubiquitous non-equilibrium phenomenon. In the course similar to that given by the author in 2006 in Warwick [45], we discuss lessons which have been learned…

This note is an expanded and updated version of our entry with the same title for the 2006 Encyclopedia of Mathematical Physics. We give a brief overview of graded Poisson algebras, their main properties and their main applications, in the…

Physical notions of stochastic resonance for potential diffusions in periodically changing double-well potentials such as the spectral power amplification have proved to be defective. They are not robust for the passage to their effective…

We construct a general procedure for the Quasi Likelihood Analysis applied to a multivariate point process on the real half line in an ergodic framework. More precisely, we assume that the stochastic intensity of the underlying model…

This paper explores an intervention that emphasizes expert practice using spaced recall. Interviews were performed with two students who were shown physics solutions, and were asked to repeatedly recall the solutions over a period of weeks.…

In the present research, a variational technique to modifying the Poisson equation is presented, expanding its modelling capabilities to include a wider range of physical processes and resonant structures. The study examines the…

The generic behavior of quantum systems has long been of theoretical and practical interest. Any quantum process is represented by a sequence of quantum channels. We consider general ergodic sequences of stochastic channels with arbitrary…

This paper consists of four parts. In the first part, we explain what eigenvalues we are interested in and show the difficulties of the study on the first (non-trivial) eigenvalue through examples. In the second part, we present some (dual)…

The notion of a successful coupling of Markov processes, based on the idea that both components of the coupled system ``intersect'' in finite time with probability one, is extended to cover situations when the coupling is unnecessarily…

These lecture notes on Generalised Parton Distributions aim at providing a general picture of the field on the theoretical and phenomenological sides to master and Ph.D. students. They go along with the lecture given at the Baryon…

What should these lectures be? The subject assigned to us is so broad that many books can be written about it. So, in planning these lectures I had several options. One would be to focus on a narrow subset of topics and to cover them in…

Strong invariance principles describe the error term of a Brownian approximation of the partial sums of a stochastic process. While these strong approximation results have many applications, the results for continuous-time settings have…

The bifurcation theory of ordinary differential equations (ODEs), and its application to deterministic population models, are by now well established. In this article, we begin to develop a complementary theory for diffusion-like…

Diffusion models have emerged from various theoretical and methodological perspectives, each offering unique insights into their underlying principles. In this work, we provide an overview of the most prominent approaches, drawing attention…

Poisson algebras have become an essential topic in mathematics with a rich structure and wide applicability. Despite numerous resources available on Poisson structures, the algebraic side of the story remains relatively less explored. This…

The main goal of these notes is to give an introduction to the mathematics of quantum noise and some of its applications in non-equilibrium statistical mechanics. We start with some reminders from the theory of classical stochastic…

Fractional Poisson processes, a rapidly growing area of non-Markovian stochastic processes, are useful in statistics to describe data from counting processes when waiting times are not exponentially distributed. We show that the fractional…

We develop a Perron-Frobenius type theory for products of random quantum channels acting on finite-dimensional matrix algebras sampled from a stationary and ergodic stochastic process, which, in keeping with the literature, we call ergodic…

The often debated issue of `ratios of small numbers of events' is approached from a probabilistic perspective, making a clear distinction between the predictive problem (forecasting numbers of events we might count under well stated…

We investigate mathematically a nonlinear approximation type approach recently introduced in [A. Ammar et al., J. Non-Newtonian Fluid Mech., 2006] to solve high dimensional partial differential equations. We show the link between the…