Limit theorems for sums of dependent random variables occurring in statistical mechanics

1980 ◽  
Vol 51 (2) ◽  
pp. 153-169 ◽  
Author(s):  
Richard S. Ellis ◽  
Charles M. Newman ◽  
Jay S. Rosen
Keyword(s):  
Statistical Mechanics ◽  
Limit Theorems ◽  
Random Variables ◽  
Dependent Random Variables

Laws of large numbers for q-dependent random variables and nonextensive statistical mechanics

2017 ◽  
Vol 31 (15) ◽  
pp. 1750117
Author(s):  
Marco A. S. Trindade
Keyword(s):  
Statistical Mechanics ◽  
Stochastic Processes ◽  
Law Of Large Numbers ◽  
Random Variables ◽  
Nonextensive Statistical Mechanics ◽  
Dependent Random Variables ◽  
Strong Law ◽  
Laws Of Large Numbers ◽  
Large Numbers

In this work, we prove a weak law and a strong law of large numbers through the concept of [Formula: see text]-product for dependent random variables, in the context of nonextensive statistical mechanics. Applications for the consistency of estimators are presented and connections with stochastic processes are discussed.

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