Intersections of random sets

نویسندگان

چکیده

Abstract We consider a variant of classical coverage process, the Boolean model in $\mathbb{R}^d$ . Previous efforts have focused on convergence unoccupied region containing origin to well-studied limit C study intersection sets centered at points Poisson point process confined unit ball. Using coupling between and original model, we show that scaled converges weakly same Along way, present some tools for studying statistics class models.

برای دانلود باید عضویت طلایی داشته باشید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Random Intersections of Thick Cantor Sets

Let C1, C2 be Cantor sets embedded in the real line, and let τ1, τ2 be their respective thicknesses. If τ1τ2 > 1, then it is well known that the difference set C1 − C2 is a disjoint union of closed intervals. B. Williams showed that for some t ∈ int(C1−C2), it may be that C1∩ (C2 + t) is as small as a single point. However, the author previously showed that generically, the other extreme is tru...

متن کامل

Intersections of Shifted Sets

We consider shifts of a set A ⊆ N by elements from another set B ⊆ N, and prove intersection properties according to the relative asymptotic size of A and B. A consequence of our main theorem is the following: If A = {an} is such that an = o(n k/k−1), then the k-recurrence set Rk(A) = {x | |A∩ (A+ x)| > k} contains the distance sets of some arbitrarily large finite sets.

متن کامل

Intersections of Random Lines

We have three overlapping planar sets within a bounded window. These sets do not have to be convex, or even connected domains. We find a simple expression for the probability that random straight lines across two of the sets intersect within the third. The lines are taken uniformly at random from beams of parallel lines, with the orientations of the beams from an arbitrary joint distribution. T...

متن کامل

Intersections of Sets of Distance

We isolate conditions on the relative asymptotic size of sets of natural numbers A,B that guarantee a nonempty intersection of the corresponding sets of distances. Such conditions apply to a large class of zero density sets. We also show that a variant of Khintchine’s Recurrence Theorem holds for all infinite sets A = {a1 < a2 < . . .} where ann n3/2.

متن کامل

Intersections with random geometric objects

We present a systematic study of the expected complexity of the intersection of geometric objects. We first study the expected size of the intersection between a random Voronoi diagram and a generic geometric object that consists of a finite collection of line segments in the plane. Using this result, we explore the intersection complexity of a random Voronoi diagram with the following target o...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

ژورنال

عنوان ژورنال: Journal of Applied Probability

سال: 2022

ISSN: ['1475-6072', '0021-9002']

DOI: https://doi.org/10.1017/jpr.2021.34