Related papers: The concentration inequality for a discrete height…
This work investigates the influence of a generic anomalous diffusion model on mass convection in a fluid-saturated porous medium, focusing on superdiffusive regimes. A mathematical model is developed, and tability analyses - both linear…
Structural defects are ubiquitous in condensed matter, and not always a nuisance. For example, they underlie phenomena such as Anderson localization and hyperuniformity, and they are now being exploited to engineer novel materials. Here, we…
Our main contribution is a concentration inequality for the symmetric volume difference of a $ C^2 $ convex body with positive Gaussian curvature and a circumscribed random polytope with a restricted number of facets, for any probability…
We present precise multilevel exponential concentration inequalities for polynomials in Ising models satisfying the Dobrushin condition. The estimates have the same form as two-sided tail estimates for polynomials in Gaussian variables due…
We prove concentration inequalities of the form $P(Y \ge t) \le \exp(-B(t))$ for a random variable $Y$ with mean zero and variance $\sigma^2$ using a coupling technique from Stein's method that is so-called approximate zero bias couplings.…
We prove an extension of McDiarmid's inequality for metric spaces with unbounded diameter. To this end, we introduce the notion of the {\em subgaussian diameter}, which is a distribution-dependent refinement of the metric diameter. Our…
This article investigates a distributed aggregative optimization problem subject to coupled affine inequality constraints, in which local objective functions depend not only on their own decision variables but also on an aggregation of all…
Diffusion of self-propelled particles in the presence of randomly distributed obstacles in three dimensions is studied using molecular dynamics simulations. It is found that depending on the magnitude of the propelling force and the…
We prove here the concentration of measure inequality for Lipschitz function on the Hamming cube with values in any Banach spaces of finite cotype.
It is well-known that measures whose density is the form $e^{-V}$ where $V$ is a uniformly convex potential on $\RR^n$ attain strong concentration properties. In search of a notion of log-concavity on the discrete hypercube, we consider…
Let $\mathsf{N}_{\rm d}\left[X\right]=\frac{1}{2\pi {\rm e}}{\rm e}^{2\mathsf{H}\left[X\right]}$ denote the entropy power of the discrete random variable $X$ where $\mathsf{H}\left[X\right]$ denotes the discrete entropy of $X$. In this…
We explore the question whether Lipschitz functions of random variables under various forms of negative correlation satisfy concentration bounds similar to McDiarmid's inequality for independent random variables. We prove such a…
Inertial microfluidics has been limited to dilute particle concentrations due to defocusing (spreading out) at high particle concentrations. We observe a counterintuitive shift of focusing to the outer curved wall under high concentration…
We present a theoretical and experimental study of light transport in disordered media with strongly heterogeneous distribution of scatterers formed via non-scattering regions. Step correlations induced by quenched disorder are found to…
We demonstrate that the arbitrarily weak quenched disorder on the surface of a system of continuous symmetry destroys long range order in the bulk, and, instead, quasi-long range order emerges. Correlation functions are calculated exactly…
The depletion potential between two hard spheres in a solvent of thin hard disclike platelets is investigated by using either the Derjaguin approximation or density functional theory. Particular attention is paid to the density dependence…
In this note we prove Minami's estimate for a class of discrete alloy-type models with a sign-changing single-site potential of finite support. We apply Minami's estimate to prove Poisson statistics for the energy level spacing. Our result…
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…
Consider the standard nonparametric regression model and take as estimator the penalized least squares function. In this article, we study the trade-off between closeness to the true function and complexity penalization of the estimator,…
We introduce a version of Stein's method for proving concentration and moment inequalities in problems with dependence. Simple illustrative examples from combinatorics, physics, and mathematical statistics are provided.