Opis

• Tytuł:
  Finite random coverings of one-complexes and the Euler characteristic
• Twórca:
  Pullen, J.;
  Komendarczyk, Rafał
• Opis:
  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.
• Dostępność obiektu:
  Dostęp otwarty
• Prawa:
  Prawa autorskie (c) 2015 Topological Methods in Nonlinear Analysis
• Data:
  2015.03.01
• Typ:
  info:eu-repo/semantics/article;
  info:eu-repo/semantics/publishedVersion;
  Recenzowany artykuł
• Język:
  angielski
• Źródło:
  Topological Methods in Nonlinear Analysis; Vol 45, No 1 (March 2015); 129 - 156;
  1230-3429
• Wydawca:
  Nicolaus Copernicus University in Toruń
• Relacja: https://apcz.umk.pl/TMNA/article/view/TMNA.2015.008/5343
• Temat i słowa kluczowe:
  Complete coverage probability;
  random complexes;
  nerves;
  Vietoris--Rips complex;
  Primary 76W05;
  57M25;
  Secondary 58F18;
  58A10
• Identyfikator: https://apcz.umk.pl/TMNA/article/view/TMNA.2015.008
• Dostawca danych:
  Akademicka Platforma Czasopism
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