Characterization of the smooth Rényi Entropy Using Majorization

This paper unveils a new connection between majorization theory and the smooth Rényi entropy of order α. We completely characterize the subprobability distribution that attains the infimum included in the definition of the smooth Rényi entropy H_α^ε(p) of order α by using the notions of majorization and the Schur convexity/concavity, where p denotes a probability distribution on a discrete alphabet and ε ϵ [0,1) is an arbitrarily given constant. We can apply the obtained result to characterization of asymptotic behavior of 1/n H_α^ε(p) as n → ∞ for general sources satisfying the strong converse property.