Central Limit Theorem and Law of Large Numbers in the Mean

1982 ◽  
Vol 26 (4) ◽  
pp. 813-815
Author(s):  
V. M. Kruglov
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Central Limit ◽  
Law Of Large Numbers ◽  
Large Numbers ◽  
The Mean

The Central Limit Theorem and the Law of Large Numbers for Pair-Connectivity in Bernoulli Trees

1989 ◽  
Vol 3 (4) ◽  
pp. 477-491
Author(s):  
Kyle T. Siegrist ◽  
Ashok T. Amin ◽  
Peter J. Slater
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Central Limit ◽  
Law Of Large Numbers ◽  
Network Reliability ◽  
Random Variable ◽  
The Central Limit Theorem ◽  
Large Numbers ◽  
The Mean ◽  
The Law

Consider the standard network reliability model in which each edge of a given (n, m)-graph G is deleted, independently of all others, with probability q = 1– p (0 <p < 1). The pair-connectivity random variable X is defined to be the number of connected pairs of vertices that remain in G. The mean of X has been proposed as a measure of reliability for failure-prone communications networks in which the edge deletions correspond to failures of the communications links. We consider deviations from the mean, the law of large numbers, and the central limit theorem for X as n → ∞. Some explicit results are obtained when G is a tree using martingale difference sequences. Stars and paths are treated in detail.

scholarly journals The time to absorption in Λ-coalescents

2018 ◽  
Vol 50 (A) ◽  
pp. 177-190
Author(s):  
Götz Kersting ◽  
Anton Wakolbinger
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Central Limit ◽  
Counting Process ◽  
Law Of Large Numbers ◽  
Large Numbers

Abstract We present a law of large numbers and a central limit theorem for the time to absorption of Λ-coalescents with dust started from n blocks, as n→∞. The proofs rely on an approximation of the logarithm of the block-counting process by means of a drifted subordinator.

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