Holes and islands in random point sets
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F22%3A10436868" target="_blank" >RIV/00216208:11320/22:10436868 - isvavai.cz</a>
Result on the web
<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=I0Z54R1w__" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=I0Z54R1w__</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1002/rsa.21037" target="_blank" >10.1002/rsa.21037</a>
Alternative languages
Result language
angličtina
Original language name
Holes and islands in random point sets
Original language description
For (Formula presented.), let S be a set of points in (Formula presented.) in general position. A set I of k points from S is a k-island in S if the convex hull (Formula presented.) of I satisfies (Formula presented.). A k-island in S in convex position is a k-hole in S. For (Formula presented.) and a convex body (Formula presented.) of volume 1, let S be a set of n points chosen uniformly and independently at random from K. We show that the expected number of k-holes in S is in (Formula presented.). Our estimate improves and generalizes all previous bounds. In particular, we estimate the expected number of empty simplices in S by (Formula presented.). This is tight in the plane up to a lower-order term. Our method gives an asymptotically tight upper bound (Formula presented.) even in the much more general setting, where we estimate the expected number of k-islands in S.
Czech name
—
Czech description
—
Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10101 - Pure mathematics
Result continuities
Project
<a href="/en/project/GA18-19158S" target="_blank" >GA18-19158S: Algorithmic, structural and complexity aspects of geometric and other configurations</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2022
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Random Structures and Algorithms
ISSN
1042-9832
e-ISSN
—
Volume of the periodical
60
Issue of the periodical within the volume
3
Country of publishing house
US - UNITED STATES
Number of pages
19
Pages from-to
308-326
UT code for WoS article
000671793500001
EID of the result in the Scopus database
2-s2.0-85109417804