This paper deals with the union set of a stationary Poisson process cylinders in Rn having an (n−m)-dimensional base and m-dimensional direction space, where m∈{0,1,…,n−1} n≥2. The concept simultaneously generalises those Boolean model hyperplane or m-flat process. Under very general conditions on typical cylinder Berry-Esseen bound for volume within sequence growing test sets is derived. Assum...

Given a Gromov-hyperbolic group G $G$ endowed with finite symmetric generating set, we study the statistics of counting measures on spheres associated Cayley graph under linear representations . More generally, obtain weak law large numbers for subadditive functions, echoing classical Fekete lemma. For strongly irreducible and proximal representations, prove central limit theorem Berry–Esseen t...

Suppose that X1, . . . ,Xn are independent, identically-distributed random variables of mean zero and variance one. Assume that E|X1| ≤ δ4. We observe that there exist many choices of coefficients θ1, . . . , θn ∈ R with ∑ j θ 2 j = 1 for which sup α,β∈R α<β ∣∣∣∣∣ P  α ≤ n ∑ j=1 θjXj ≤ β   − 1 √ 2π ∫ β α e−t 2/2dt ∣∣∣∣∣ ≤ Cδ 4 n , (1) where C > 0 is a universal constant. Inequality (1) shou...

We consider a random walk Sk with i.i.d. steps on compact group equipped bi-invariant metric. prove quantitative ergodic theorems for the sum ? k=1Nf(Sk) Hölder continuous test functions f, including central limit theorem, law of iterated logarithm and an almost sure approximation by Wiener process, provided that distribution converges to Haar measure in p-Wasserstein metric fast enough. As exa...

This paper analyzes the maximal achievable rate for a given blocklength and error probability over multiple-antenna ambient backscatter channel. The result consists of finite channel coding achievability bound converse legacy system with alphabet constraints multiple-input-multiple-output based on Neyman-Pearson test, Berry-Esseen theorem, Mellin transform. Then, we derive closed-form expressio...

We give error bounds which demonstrate optimal rates of convergence in the CLT for the total covered volume and the number of isolated shapes, for germ-grain models with fixed grain radius over a binomial point process of n points in a toroidal spatial region of volume n. The proof is based on Stein's method via size-biased couplings. 1. Introduction. Given a collection of n independent uniform...