Related papers: Benford's Law and Continuous Dependent Random Vari…
A branching process in random environment $(Z_n, n \in \N)$ is a generalization of Galton Watson processes where at each generation the reproduction law is picked randomly. In this paper we give several results which belong to the class of…
This is the first part of a work devoted to the study of linear Mahler systems in several variables from the perspective of transcendence and algebraic independence. We prove two main results concerning systems that are regular singular at…
How much dependence is there in the prime factorization of a random integer distributed uniformly from 1 to n? How much dependence is there in the decomposition into cycles of a random permutation of n points? What is the relation between…
The long-term behavior of a supercritical branching random walk can be described and analyzed with the help of Biggins' martingales, parametrized by real or complex numbers. The study of these martingales with complex parameters is a rather…
The dynamics of nonlinear conservation laws have long posed fascinating problems. With the introduction of some nonlinearity, e.g. Burgers' equation, discontinuous behavior in the solutions is exhibited, even for smooth initial data. The…
We want to select the best systems out of a given set of systems (or rank them) with respect to their expected performance. The systems allow random observations only and we assume that the joint observation of the systems has a…
This paper is concerned with cross-sectional dependence arising because observations are interconnected through an observed network. Following Doukhan and Louhichi (1999), we measure the strength of dependence by covariances of nonlinearly…
We establish strong invariance principles for sums of stationary and ergodic processes with nearly optimal bounds. Applications to linear and some nonlinear processes are discussed. Strong laws of large numbers and laws of the iterated…
We are interested in the randomly biased random walk on the supercritical Galton--Watson tree. Our attention is focused on a slow regime when the biased random walk $(X_n)$ is null recurrent, making a maximal displacement of order of…
We study the problem of deriving policies, or rules, that when enacted on a complex system, cause a desired outcome. Absent the ability to perform controlled experiments, such rules have to be inferred from past observations of the system's…
In systems which exhibit deterministic diffusion, the gross parameter dependence of the diffusion coefficient can often be understood in terms of random walk models. Provided the decay of correlations is fast enough, one can ignore memory…
Random matrices whose entries come from a stationary Gaussian process are studied. The limiting behavior of the eigenvalues as the size of the matrix goes to infinity is the main subject of interest in this work. It is shown that the…
Consider a branching random walk in which the offspring distribution and the moving law both depend on an independent and identically distributed random environment indexed by the time.For the normalised counting measure of the number of…
Motivated by the study of asymptotic behaviour of the bandit problems, we obtain several strategy-driven limit theorems including the law of large numbers, the large deviation principle, and the central limit theorem. Different from the…
Statistical systems are conceived from the standpoint of statistical mechanics, as made of a (generally large) number of identical units and exhibiting a (generally large) number of different configurations (microstates), among which only…
Addressing selection bias in latent variable causal discovery is important yet underexplored, largely due to a lack of suitable statistical tools: While various tools beyond basic conditional independencies have been developed to handle…
We study the error of the number of points of a unimodular lattice that fall in a strictly convex and analytic set having the origin and that is dilated by a factor $t$. The aim is to generalize the result of a previous article. We first…
Some probabilistic aspects of the number variance statistic are investigated. Infinite systems of independent Brownian motions and symmetric alpha-stable processes are used to construct new examples of processes which exhibit both divergent…
Concentration of measure is a phenomenon in which a random variable that depends in a smooth way on a large number of independent random variables is essentially constant. The random variable will "concentrate" around its median or…
We apply random matrix theory to study the impact of measurement uncertainty on dynamic mode decomposition. Specifically, when the measurements follow a normal probability density function, we show how the moments of that density propagate…