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By molecular dynamic simulations we study a system of particles interacting through a continuous isotropic pairwise core-softened potential consisting of a repulsive shoulder and an attractive well. The model displays a phase diagram with…
The aim of this paper is to prove an improved version of the bounded differences inequality for matrix valued functions, by developing the methods of Mackey et al.: "Matrix Concentration Inequalities via the Method of Exchangeable Pairs".…
In this work we show that under specific anomalous diffusion conditions, chemical systems can produce well-ordered self-similar concentration patterns through a diffusion-driven instability. We also find spiral patterns and patterns with…
We investigate the dynamics of a single, overdamped colloidal particle, which is driven by a constant force through a one-dimensional periodic potential. We focus on systems with large barrier heights where the lowest-order cumulants of the…
The problem of a bouncing ball on a non-planar surface is investigated. We discovered that surface undulation adds a horizontal component to the impact force, which acquires a random character. Some aspects of Brownian motion are found in…
In this paper our aim is to present some monotonicity and convexity properties for the one dimensional regularization of the Coulomb potential, which has applications in the study of atoms in magnetic fields and which is in fact a…
We prove generalised concentration inequalities for a class of scaled self-bounding functions of independent random variables, referred to as ${(M,a,b)}$ self-bounding. The scaling refers to the fact that the component-wise difference is…
This paper considers a distributionally robust chance constraint model with a general ambiguity set. We show that a sample based approximation of this model converges under suitable sufficient conditions. We also show that upper and lower…
We derive two concentration inequalities for linear functions of log-concave distributions: an enhanced version of the classical Brascamp--Lieb concentration inequality, and an inequality quantifying log-concavity of marginals in a manner…
We derive concentration inequalities for maxima of empirical processes associated with Poisson point processes. The proofs are based on a careful application of Ledoux's entropy method. We demonstrate the utility of the obtained…
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 Lp Poincare inequalities for functions on the discrete cube and their discrete gradient. We thus recover an exponential inequality and the concentration phenomenon for the uniform probability on the cube first obtained by Bobkov…
A metric probability space $(\Omega,d)$ obeys the ${\it concentration\; of\; measure\; phenomenon}$ if subsets of measure $1/2$ enlarge to subsets of measure close to 1 as a transition parameter $\epsilon$ approaches a limit. In this paper…
We prove an exponential deviation inequality for the convex hull of a finite sample of i.i.d. random points with a density supported on an arbitrary convex body in $\R^d$, $d\geq 2$. When the density is uniform, our result yields rate…
We study the influence of a point defect on the profile of a growing surface in the single-step growth model. We employ the mapping to the asymmetric exclusion model with blockage, and using Bethe-Ansatz eigenfunctions as a starting…
We give a distribution-dependent concentration inequality for functions of independent variables. The result extends Bernstein's inequality from sums to more general functions, whose variation in any argument does not depend too much on the…
The potential risk of privacy leakage prevents users from sharing their honest opinions on social platforms. This paper addresses the problem of privacy preservation if the query returns the histogram of rankings. The framework of…
We obtain a Bernstein type Gaussian concentration inequality for martingales. Our inequality improves the Azuma-Hoeffding inequality for moderate deviations $x$. Following the work of McDiarmid (1989), Talagrand (1996) and Boucheron, Lugosi…
We prove several different anti-concentration inequalities for functions of independent Bernoulli-distributed random variables. First, motivated by a conjecture of Alon, Hefetz, Krivelevich and Tyomkyn, we prove some "Poisson-type"…
The analysis of panel count data has garnered considerable attention in the literature, leading to the development of multiple statistical techniques. In inferential analysis, most works focus on leveraging estimating equation-based…