Related papers: Concentration inequalities for measures of a Boole…
A stationary Boolean model is the union set of random compact particles which are attached to the points of a stationary Poisson point process. For a stationary Boolean model with convex grains we consider a recently developed collection of…
In this work we derive multi-level concentration inequalities for polynomial functions in independent random variables with a $\alpha$-sub-exponential tail decay. A particularly interesting case is given by quadratic forms $f(X_1, \ldots,…
We study a model of directed polymers in random environment in dimension $1+d$, given by a Brownian motion in a Poissonian potential. We study the effect of the density and the strength of inhomogeneities, respectively the intensity…
In the spherical Poisson Boolean model, one takes the union of random balls centred on the points of a Poisson process in Euclidean $d$-space with $d \geq 2$. We prove that whenever the radius distribution has a finite $d$-th moment, there…
The purpose of this dissertation is to introduce a version of Stein's method of exchangeable pairs to solve problems in measure concentration. We specifically target systems of dependent random variables, since that is where the power of…
We prove Bernstein-type matrix concentration inequalities for linear combinations with matrix coefficients of binary random variables satisfying certain $\ell_\infty$-independence assumptions, complementing recent results by Kaufman, Kyng…
A generalization of the Bernstein matrix concentration inequality to random tensors of general order is proposed. This generalization is based on the use of Einstein products between tensors, from which a strong link can be established…
Using the method of transportation-information inequality introduced in \cite{GLWY}, we establish Bernstein type's concentration inequalities for empirical means $\frac 1t \int_0^t g(X_s)ds$ where $g$ is a unbounded observable of the…
The paper considers a Cox process where the stochastic intensity function for the Poisson data model is itself a non-homogeneous Poisson process. We show that it is possible to obtain the marginal data process, namely a non-homogeneous…
We simulate correlation measurements of entangled photons numerically. The model employed is strictly local. The correlation is determined by its classical expression with one decisive difference: we sum up coincidences for each pair…
In its continuous version, the entropy functional measuring the information content of a given probability density may be plagued by a "measure" problem that results from improper weighting of phase space. This issue is addressed…
The aim of this work is to simulate the pollutants transport in buildings. Focusing mainly on the presence of CO2, firstly we resolve the airflow equations for two typical validation cases, the Rao case and the IEA case. These numerical…
This paper gives a review of concentration inequalities which are widely employed in non-asymptotical analyses of mathematical statistics in a wide range of settings, from distribution-free to distribution-dependent, from sub-Gaussian to…
We prove concentration inequalities for functions of independent random variables {under} sub-gaussian and sub-exponential conditions. The utility of the inequalities is demonstrated by an extension of the now classical method of Rademacher…
A class of k-particle observables in a two-mode system of Bose particles is characterized by typicality: if the state of the system is sampled out of a suitable ensemble, an experimental measurement of that observable yields (almost) always…
This work studies nonparametric Bayesian estimation of the intensity function of an inhomogeneous Poisson point process in the important case where the intensity depends on covariates, based on the observation of a single realisation of the…
Concentration of measure is studied, and obtained, for stable and related random vectors.
In this article, we consider a configuration of weighted random balls in $\mathbb{R}^d$ generated according to a Poisson point process. The model investigated exhibits inhomogeneity, as well as dependence between the centers and the radii…
We investigate concentration inequalities for Dirichlet and Multinomial random variables.
This paper introduces a new stochastic process with values in the set Z of integers with sign. The increments of process are Poisson differences and the dynamics has an autoregressive structure. We study the properties of the process and…