##  [Large Deviations Theory](/large-deviations-theory) 

  ##  [Large Deviations Theory](https://information.quantumdictionary.io/large-deviations-theory-0) 

  

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**Information & Communication Dictionary**

 







 

 

 

 



 

 

 

 

Definition

Mathematical theory that characterizes the exponential decay rates of probabilities of rare events for a family or sequence of stochastic processes or random variables, typically by establishing a Large Deviations Principle (LDP) that provides asymptotic upper and lower bounds of the form P(X_n ∈ A) ≍ exp(-n I(A)) where I is a rate function describing the dominant exponential rate.