Related papers: Concentration inequalities for functionals of Pois…
It is well known that the Fourier--Bohr coefficients of regular model sets exist and are uniformly converging, volume-averaged exponential sums. Several proofs for this statement are known, all of which use fairly abstract machinery. For…
The intrinsic volumes of a convex cone are geometric functionals that return basic structural information about the cone. Recent research has demonstrated that conic intrinsic volumes are valuable for understanding the behavior of random…
Typical weighted random simplices $Z_{\mu}$, $\mu\in(-2,\infty)$, in a Poisson-Delaunay tessellation in $\mathbb{R}^n$ are considered, where the weight is given by the $(\mu+1)$st power of the volume. As special cases this includes the…
We consider a stationary Poisson hyperplane process with given directional distribution and intensity in $d$-dimensional Euclidean space. Generalizing the zero cell of such a process, we fix a convex body $K$ and consider the intersection…
We study visibility inside the vacant set of three models in $\mathbb R^d$ with slow decay of spatial correlations: Brownian interlacements, Poisson cylinders and Poisson-Boolean models. Let $Q_x$ be the radius of the largest ball centered…
Using Talagrand's concentration inequality on the discrete cube {0,1}^m we show that given a real-valued function Z(x)on {0,1}^m that satisfies certain monotonicity conditions one can control the deviations of Z(x) above its median by a…
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…
We prove that, in the coupon collector's problem, the point processes given by the times of $r$-th arrivals for coupons of each type, centered and normalized in a proper way, converge toward a non-homogeneous Poisson point process. This…
Excursion sets of Poisson shot noise processes are a prominent class of random sets. We consider a specific class of Poisson shot noise processes whose excursion sets within compact convex observation windows are almost surely polyconvex.…
A natural model for the approximation of a convex body $K$ in $\mathbb{R}^d$ by random polytopes is obtained as follows. Take a stationary Poisson hyperplane process in the space, and consider the random polytope $Z_K$ defined as the…
Let $\mathbf{W}=(W_1,W_2,...,W_k)$ be a random vector with nonnegative coordinates having nonzero and finite variances. We prove concentration inequalities for $\mathbf{W}$ using size biased couplings that generalize the previous univariate…
The martingale method is used to establish concentration inequalities for a class of dependent random sequences on a countable state space, with the constants in the inequalities expressed in terms of certain mixing coefficients. Along the…
Direct numerical simulations are used to study the interaction of a stream of small heavy inertial particles with the laminar and turbulent wakes of an immobile sphere facing an incompressible uniform inflow. Particles that do not collide…
While classical concentration inequalities are typically restricted to two special cases -- independence and martingale difference sequences -- we extend concentration inequalities to a much broader class of stochastic processes by relaxing…
The paper investigates uniform convergence of wavelet expansions of Gaussian random processes. The convergence is obtained under simple general conditions on processes and wavelets which can be easily verified. Applications of the developed…
We study a parametric class of isotropic but not necessarily stationary Poisson hyperplane tessellations in n-dimensional Euclidean space. Our focus is on the volume of the zero cell, i.e. the cell containing the origin. As a main result,…
We give a concentration inequality based on the premise that random variables take values within a particular region. The concentration inequality guarantees that, for any sequence of correlated random variables, the difference between the…
Concentration invariance of cyclic species in the irreversible polymerization is examined. The simulation shows that the invariance theorem holds in good approximation for the irreversible process also. The physical soundness of the…
The set of volumes of stable surfaces does have accumulation points. In this paper, we study this phenomenon for surfaces with one cyclic quotient singularity, towards answering the question under which conditions we can still have…
Random arrangements of points in the plane, interacting only through a simple hard core exclusion, are considered. An intensity parameter controls the average density of arrangements, in analogy with the Poisson point process. It is proved…