Object's details: Finite random coverings of one-complexes and the Euler characteristic

Provider:Akademicka Platforma Czasopism

Description

Title:
Finite random coverings of one-complexes and the Euler characteristic
Creator:
Pullen, J.;
Komendarczyk, Rafał
Description:
This article presents an algebraic topology perspective on the problem of finding a complete coverage probability of a one dimensional domain $X$ by a random covering, and develops techniques applicable to the problem beyond the one dimensional case. In particular we obtain a general formula for the chance that a collection of finitely many compact connected random sets placed on $X$ has a union equal to $X$. The result is derived under certain topological assumptions on the shape of the covering sets (the covering ought to be {\em good}, which holds if the diameter of the covering elements does not exceed a certain size), but no a priori requirements on their distribution. An upper bound for the coverage probability is also obtained as a consequence of the concentration inequality. The techniques rely on a formulation of the coverage criteria in terms of the Euler characteristic of the nerve complex associated to the random covering.
Object availability:
free access
Rights:
Prawa autorskie (c) 2015 Topological Methods in Nonlinear Analysis
Date:
2015.03.01
Type:
info:eu-repo/semantics/article;
info:eu-repo/semantics/publishedVersion;
Recenzowany artykuł
Language:
English
Source:
Topological Methods in Nonlinear Analysis; Vol 45, No 1 (March 2015); 129 - 156;
1230-3429
Publisher:
Nicolaus Copernicus University in Toruń
Relation: https://apcz.umk.pl/TMNA/article/view/TMNA.2015.008/5343
Subject:
Complete coverage probability;
random complexes;
nerves;
Vietoris--Rips complex;
Primary 76W05;
57M25;
Secondary 58F18;
58A10
Identifier: https://apcz.umk.pl/TMNA/article/view/TMNA.2015.008
Data provider:
Akademicka Platforma Czasopism

Similar objects

Finite random coverings of one-complexes and the Euler characteristic

Creator:Pullen, J. | Komendarczyk, Rafał

Date:2015.03.01

Type:other

Knot invariants coming from pre-image indices

Creator:Chen, Xing | Zhao, Xuezhi

Date:2020.11.27

Type:other

Parameter dependent pull-back of closed differential forms and invariant integrals

Creator:Mawhin, Jean

Date:2005.09.01

Type:other

Morphology of the sacral plexus of the tapir

Creator:Arłamowska-Palider, A.

Date:1969.12.31 | 1969

Type:other

The effect of ischemic preconditioning on the cardiac autonomic nervous system after exercise: A systematic review and meta-analysis: Ischemic preconditioning affects the cardiac autonomic nervous system

Date:2024.11.17

Type:text

Effects of renal nerve stimulation on intrarenal blood flow in rats with intact or inactivated NO synthases

Creator:Walkowska, Agnieszka | Badzyńska, Bożena | Kompanowska-Jezierska, Elżbieta | Johns, EJ | Sadowski, Janusz

Date:2005.12.31 | 2005

Type:other

Frey syndrome

Date:2022.08.23

Type:text

Communications between the facial and trigeminal nerves in certain mammals

Creator:Bowden, R. E. M. | Mahran, Z. Y. | Gooding, M. R.

Date:1960.12.31 | 1960

Type:other

Federacja Bibliotek Cyfrowych

Object's details: Finite random coverings of one-complexes and the Euler characteristic

Description

Similar objects