Zobrazeno 1 - 10
of 130
pro vyhledávání: '"Yukich, J. E."'
Autor:
Schulte, Matthias, Yukich, J. E.
We employ stabilization methods and second order Poincar\'e inequalities to establish rates of multivariate normal convergence for a large class of vectors $(H_s^{(1)},...,H_s^{(m)})$, $s \geq 1$, of statistics of marked Poisson processes on $\mathbb
Externí odkaz:
http://arxiv.org/abs/2103.00625
Autor:
Calka, Pierre, Yukich, J. E.
We consider the convex hull of the perturbed point process comprised of $n$ i.i.d. points, each distributed as the sum of a uniform point on the unit sphere $\S^{d-1}$ and a uniform point in the $d$-dimensional ball centered at the origin and of radi
Externí odkaz:
http://arxiv.org/abs/1912.10304
Autor:
Schulte, Matthias, Yukich, J. E.
Given a vector $F=(F_1,\dots,F_m)$ of Poisson functionals $F_1,\dots,F_m$, we investigate the proximity between $F$ and an $m$-dimensional centered Gaussian random vector $N_\Sigma$ with covariance matrix $\Sigma\in\mathbb{R}^{m\times m}$. Apart from
Externí odkaz:
http://arxiv.org/abs/1803.11059
We establish presumably optimal rates of normal convergence with respect to the Kolmogorov distance for a large class of geometric functionals of marked Poisson and binomial point processes on general metric spaces. The rates are valid whenever the g
Externí odkaz:
http://arxiv.org/abs/1702.00726
Publikováno v:
Journal of Applied Probability, 2020 Jun 01. 57(2), 679-702.
Externí odkaz:
https://www.jstor.org/stable/48656242
Publikováno v:
The Annals of Probability, 47(2) 2019
Let $P$ be a simple,stationary point process having fast decay of correlations, i.e., its correlation functions factorize up to an additive error decaying faster than any power of the separation distance. Let $P_n:= P \cap W_n$ be its restriction to
Externí odkaz:
http://arxiv.org/abs/1606.03988
Autor:
Calka, Pierre, Yukich, J. E.
Let K be a convex set in R d and let K $\lambda$ be the convex hull of a homogeneous Poisson point process P $\lambda$ of intensity $\lambda$ on K. When K is a simple polytope, we establish scaling limits as $\lambda$ $\rightarrow$ $\infty$ for the b
Externí odkaz:
http://arxiv.org/abs/1601.08025
Autor:
Thäle, Christoph, Yukich, J. E.
Publikováno v:
Bernoulli 2016, Vol. 22, No. 4, 2372-2400
This paper establishes expectation and variance asymptotics for statistics of the Poisson--Voronoi approximation of general sets, as the underlying intensity of the Poisson point process tends to infinity. Statistics of interest include volume, surfa
Externí odkaz:
http://arxiv.org/abs/1503.08963
Autor:
Xia, Aihua, Yukich, J. E.
This paper concerns the asymptotic behavior of a random variable $W_\lambda$ resulting from the summation of the functionals of a Gibbsian spatial point process over windows $Q_\lambda \uparrow R^d$. We establish conditions ensuring that $W_\lambda$
Externí odkaz:
http://arxiv.org/abs/1409.6380
Autor:
Calka, Pierre, Yukich, J. E.
Let $K_n$ be the convex hull of i.i.d. random variables distributed according to the standard normal distribution on $\R^d$. We establish variance asymptotics as $n \to \infty$ for the re-scaled intrinsic volumes and $k$-face functionals of $K_n$, $k
Externí odkaz:
http://arxiv.org/abs/1403.1010