Related papers: Correlations of multiplicative functions along det…

The aim of this paper is to give linear independence results for the values of certain series. As an application, we derive arithmetical properties of the sums of reciprocals of Fibonacci and Lucas numbers associated with certain coprime…

We prove some properties of analytic multiplicative and sub-multiplicative cocycles. The results allow to construct natural invariant analytic sets associated to complex dynamical systems.

We study two-state (dichotomous, telegraph) random ergodic continuous-time processes with dynamics depending on their past. We take into account the history of process in an explicit form by introducing an integral non-local memory term…

By studying varies dynamical processes, including coupled maps, cellular automata and coupled differential equations, on five different kinds of known networks, we found a positive relation between signal correlation and node's degree. Thus…

Universality of correlation functions obtained in parametric random matrix theory is explored in a multi-parameter formalism, through the introduction of a diffusion matrix $D_{ij}(R)$, and compared to results from a multi-parameter chaotic…

The paper studies the relationship between diffraction and dynamics for uniformly discrete ergodic point processes in real spaces. This relationship takes the form of an isometric embedding of two L^2 spaces. Diffraction (or equivalently…

We propose new concepts in order to analyze and model the dependence structure between two time series. Our methods rely exclusively on the order structure of the data points. Hence, the methods are stable under monotone transformations of…

Finding interdependency relations between (possibly multivariate) time series provides valuable knowledge about the processes that generate the signals. Information theory sets a natural framework for non-parametric measures of several…

For the challenging task of modeling multivariate time series, we propose a new class of models that use dependent Mat\'ern processes to capture the underlying structure of data, explain their interdependencies, and predict their unknown…

In this work, we are concerned with existence and uniqueness of invariant measures for path-dependent random diffusions and their time discretizations. The random diffusion here means a diffusion process living in a random environment…

Let $v$ be an odd real polynomial (i.e. a polynomial of the form $\sum_{j=1}^\ell a_jx^{2j-1}$). We utilize sets of iterated differences to establish new results about sets of the form $\mathcal…

We provide a probabilistic analysis of the banker algorithm when transition probabilities may depend on time and space. The transition probabilities evolve, as time goes by, along the trajectory of an ergodic Markovian environment, whereas…

We consider a class of stochastic dynamical networks whose governing dynamics can be modeled using a coupling function. It is shown that the dynamics of such networks can generate geometrically ergodic trajectories under some reasonable…

This paper characterizes the impact of covariate serial dependence on the non-asymptotic estimation error bound of penalized regressions (PRs). Focusing on the direct relationship between the degree of cross-correlation between covariates…

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…

We propose a new approach to temporal inference, inspired by the Pearlian causal inference paradigm - though quite different from Pearl's approach formally. Rather than using directed acyclic graphs, we make use of factored sets, which are…

A map is given showing that convolutions of independent random variables over a finite group and matrix multiplications of doubly stochastic matrices are homomorphic. As an application, a short proof is given to the theorem that the…

Testing cross-sectional independence in panel data models is of fundamental importance in econometric analysis with high-dimensional panels. Recently, econometricians began to turn their attention to the problem in the presence of serial…

So far, one-factor copulas induce conditional independence with respect to a latent factor. In this paper, we extend one-factor copulas to conditionally dependent models. This is achieved through new representations which allow to build new…

Our aim is to detect mechanistic interaction between the effects of two causal factors on a binary response, as an aid to identifying situations where the effects are mediated by a common mechanism. We propose a formalization of mechanistic…