On the Entropy Power Inequality for the Rényi Entropy of Order [0, 1]

Following a recent proof of Shannon’s entropy power inequality (EPI), a comprehensive framework for deriving various EPIs for the Rényi entropy is presented that uses transport arguments from normal densities and a change of variable by rotation. Simple arguments are given to recover the previously known Rényi EPIs and derive new ones, by unifying a multiplicative form with constant c and a modification with exponent α of previous works. In particular, for log-concave densities, we obtain a simple transportation proof of a sharp varentropy bound.

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Rényi entropy power inequality and a reverse

Studia Mathematica ◽

10.4064/sm170521-5-8 ◽

2018 ◽

Vol 242 (3) ◽

pp. 303-319 ◽

Cited By ~ 9

Author(s):

Jiange Li

Keyword(s):

Renyi Entropy ◽

Rényi Entropy ◽

Power Inequality

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Excited state Rényi entropy and subsystem distance in two-dimensional non-compact bosonic theory. Part I. Single-particle states

Journal of High Energy Physics ◽

10.1007/jhep12(2020)160 ◽

2020 ◽

Vol 2020 (12) ◽

Author(s):

Jiaju Zhang ◽

M.A. Rajabpour

Keyword(s):

Excited States ◽

Single Particle ◽

Renyi Entropy ◽

Rényi Entropy ◽

Large Momentum ◽

Particle State ◽

Two Dimensional ◽

Universal Form ◽

Conformal Field ◽

Harmonic Chain

Abstract We investigate the Rényi entropy of the excited states produced by the current and its derivatives in the two-dimensional free massless non-compact bosonic theory, which is a two-dimensional conformal field theory. We also study the subsystem Schatten distance between these states. The two-dimensional free massless non-compact bosonic theory is the continuum limit of the finite periodic gapless harmonic chains with the local interactions. We identify the excited states produced by current and its derivatives in the massless bosonic theory as the single-particle excited states in the gapless harmonic chain. We calculate analytically the second Rényi entropy and the second Schatten distance in the massless bosonic theory. We then use the wave functions of the excited states and calculate the second Rényi entropy and the second Schatten distance in the gapless limit of the harmonic chain, which match perfectly with the analytical results in the massless bosonic theory. We verify that in the large momentum limit the single-particle state Rényi entropy takes a universal form. We also show that in the limit of large momenta and large momentum difference the subsystem Schatten distance takes a universal form but it is replaced by a new corrected form when the momentum difference is small. Finally we also comment on the mutual Rényi entropy of two disjoint intervals in the excited states of the two-dimensional free non-compact bosonic theory.

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Testing homogeneity of the galaxy distribution in the SDSS using Renyi entropy

Journal of Cosmology and Astroparticle Physics ◽

10.1088/1475-7516/2021/07/019 ◽

2021 ◽

Vol 2021 (07) ◽

pp. 019

Author(s):

Biswajit Pandey ◽

Suman Sarkar

Keyword(s):

Renyi Entropy ◽

Rényi Entropy ◽

Galaxy Distribution ◽

The Galaxy ◽

Testing Homogeneity

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Conditional Rényi Entropy and the Relationships between Rényi Capacities

Entropy ◽

10.3390/e22050526 ◽

2020 ◽

Vol 22 (5) ◽

pp. 526

Author(s):

Gautam Aishwarya ◽

Mokshay Madiman

Keyword(s):

Mutual Information ◽

Renyi Entropy ◽

Rényi Entropy ◽

Basic Properties ◽

Reference Measure ◽

Definition Of ◽

Discrete Setting

The analogues of Arimoto’s definition of conditional Rényi entropy and Rényi mutual information are explored for abstract alphabets. These quantities, although dependent on the reference measure, have some useful properties similar to those known in the discrete setting. In addition to laying out some such basic properties and the relations to Rényi divergences, the relationships between the families of mutual informations defined by Sibson, Augustin-Csiszár, and Lapidoth-Pfister, as well as the corresponding capacities, are explored.

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