scholarly journals Rényi Entropy Power Inequalities via Normal Transport and Rotation

Entropy ◽  
2018 ◽  
Vol 20 (9) ◽  
pp. 641 ◽  
Author(s):  
Olivier Rioul
Keyword(s):  
Shannon’S Entropy ◽  
Renyi Entropy ◽  
Rényi Entropy ◽  
Shannon's Entropy ◽  
Change Of Variable ◽  
Power Inequality ◽  
Multiplicative Form ◽  
Normal Transport ◽  
Comprehensive Framework

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.

scholarly journals Rényi Entropy Power Inequalities via Normal Transport and Rotation

2018 ◽  
Author(s):  
Olivier Rioul
Keyword(s):  
Shannon’S Entropy ◽  
Shannon's Entropy ◽  
Change Of Variable ◽  
Power Inequality ◽  
Multiplicative Form ◽  
Normal Transport ◽  
Comprehensive Framework

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.

scholarly journals Rényi Entropy Power Inequalities via Normal Transport and Rotation

2018 ◽  
Author(s):  
Olivier Rioul
Keyword(s):  
Shannon’S Entropy ◽  
Shannon's Entropy ◽  
Change Of Variable ◽  
Power Inequality ◽  
Normal Transport ◽  
Comprehensive Framework

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.

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

2019 ◽  
Vol 65 (3) ◽  
pp. 1387-1396 ◽  
Author(s):  
Arnaud Marsiglietti ◽  
James Melbourne
Keyword(s):  
Renyi Entropy ◽  
Rényi Entropy ◽  
Power Inequality

Entropy Power Inequality for the Rényi Entropy

2015 ◽  
Vol 61 (2) ◽  
pp. 708-714 ◽  
Author(s):  
Sergey G. Bobkov ◽  
Gennadiy P. Chistyakov
Keyword(s):  
Renyi Entropy ◽  
Rényi Entropy ◽  
Power Inequality

scholarly journals Rényi entropy power inequality and a reverse

2018 ◽  
Vol 242 (3) ◽  
pp. 303-319 ◽  
Author(s):  
Jiange Li
Keyword(s):  
Renyi Entropy ◽  
Rényi Entropy ◽  
Power Inequality

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

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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