On μ-Dvoretzky random covering of the circle

Bernoulli ◽  
2021 ◽  
Vol 27 (2) ◽  
Author(s):  
Aihua Fan ◽  
Davit Karagulyan
Keyword(s):  
Random Covering

Partial and random covering times in one dimension

2001 ◽  
Vol 63 (6) ◽  
Author(s):  
Marcelo S. Nascimento ◽  
Maurício D. Coutinho-Filho ◽  
Carlos S. O. Yokoi
Keyword(s):  
One Dimension ◽  
Random Covering ◽  
Covering Times

scholarly journals Dimensions of random covering sets in Riemann manifolds

2018 ◽  
Vol 46 (3) ◽  
pp. 1542-1596 ◽  
Author(s):  
De-Jun Feng ◽  
Esa Järvenpää ◽  
Maarit Järvenpää ◽  
Ville Suomala
Keyword(s):  
Random Covering ◽  
Riemann Manifolds

A random covering of the plane by convex figures

1988 ◽  
Vol 43 (1) ◽  
pp. 2184-2186
Author(s):  
E. A. Begovatov
Keyword(s):  
Random Covering

Random covering of the circle: the size of the connected components

2003 ◽  
Vol 35 (03) ◽  
pp. 563-582 ◽  
Author(s):  
Thierry Huillet
Keyword(s):  
Joint Distribution ◽  
Random Number ◽  
Connected Components ◽  
Random Set ◽  
Asymptotic Results ◽  
Random Covering

Consider a circle of circumference 1. Throw n points at random onto this circle and append to each of these points a clockwise arc of length s. The resulting random set is a union of a random number of connected components, each with specific size. Using tools designed by Steutel, we compute the joint distribution of the lengths of the connected components. Asymptotic results are presented when n goes to ∞ and s to 0 jointly according to different regimes.

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