Proof of an algebraic central limit theorem by moment generating functions

1987 ◽  
pp. 342-347 ◽  
Author(s):  
Wilhelm von Waldenfels
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Central Limit ◽  
Generating Functions ◽  
Moment Generating Functions

scholarly journals Central Limit Theorem for Coloured Hard Dimers

2010 ◽  
Vol 2010 ◽  
pp. 1-13 ◽  
Author(s):  
Maria Simonetta Bernabei ◽  
Horst Thaler
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Central Limit ◽  
Generating Functions ◽  
Random Variables ◽  
Limit Behavior ◽  
The Central Limit Theorem ◽  
Conditional Expectations

We study the central limit theorem for a class of coloured graphs. This means that we investigate the limit behavior of certain random variables whose values are combinatorial parameters associated to these graphs. The techniques used at arriving this result comprise combinatorics, generating functions, and conditional expectations.

scholarly journals On operator-valued monotone independence

2014 ◽  
Vol 215 ◽  
pp. 151-167 ◽  
Author(s):  
Takahiro Hasebe ◽  
Hayato Saigo
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Central Limit ◽  
Generating Functions ◽  
Conditional Expectation ◽  
Random Variables ◽  
Independent Random Variables ◽  
The Central Limit Theorem ◽  
Noncommutative Version ◽  
The Moment

AbstractWe investigate operator-valued monotone independence, a noncommutative version of independence for conditional expectation. First we introduce operator-valued monotone cumulants to clarify the whole theory and show the moment-cumulant formula. As an application, one can obtain an easy proof of the central limit theorem for the operator-valued case. Moreover, we prove a generalization of Muraki’s formula for the sum of independent random variables and a relation between generating functions of moments and cumulants.

scholarly journals On operator-valued monotone independence

2014 ◽  
Vol 215 ◽  
pp. 151-167
Author(s):  
Takahiro Hasebe ◽  
Hayato Saigo
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Central Limit ◽  
Generating Functions ◽  
Conditional Expectation ◽  
Random Variables ◽  
Independent Random Variables ◽  
The Central Limit Theorem ◽  
Noncommutative Version ◽  
The Moment

AbstractWe investigate operator-valued monotone independence, a noncommutative version of independence for conditional expectation. First we introduce operator-valued monotone cumulants to clarify the whole theory and show the moment-cumulant formula. As an application, one can obtain an easy proof of the central limit theorem for the operator-valued case. Moreover, we prove a generalization of Muraki’s formula for the sum of independent random variables and a relation between generating functions of moments and cumulants.

Sign in / Sign up

Export Citation Format

Share Document