Discrete gravity on random tensor network and holographic Rényi entropy

The gravity dual of Rényi entropy

A remarkable yet mysterious property of black holes is that their entropy is proportional to the horizon area. This area law inspired the holographic principle, which was later realized concretely in gauge-gravity duality. In this context, entanglement entropy is given by the area of a minimal surface in a dual spacetime. However, discussions of area laws have been constrained to entanglement e...

Holographic entropy bound in two-dimensional gravity

Bousso’s entropy bound for two-dimensional gravity is investigated in the lightcone gauge. It is shown that due to the Weyl anomaly, the null component of the energy-momentum tensor takes a nonvanishing value, and thus, combined with the conditions that were recently proposed by Bousso, Flanagan and Marolf, a holographic entropy bound similar to Bousso’s is expected to hold in two dimensions. A...

Smooth Entropy and Rényi Entropy

The notion of smooth entropy allows a unifying, generalized formulation of privacy ampli-cation and entropy smoothing. Smooth entropy is a measure for the number of almost uniform random bits that can be extracted from a random source by probabilistic algorithms. It is known that the R enyi entropy of order at least 2 of a random variable is a lower bound for its smooth entropy. On the other ha...

On the Conditional Rényi Entropy

On Rényi entropy power inequalities

This paper is a follow-up of a recent work by Bobkov and Chistyakov, obtaining some improved Rényi entropy power inequalities (R-EPIs) for sums of independent random vectors. The first improvement relies on the same bounding techniques used in the former work, while the second significant improvement relies on additional interesting properties from matrix theory. The improvements obtained by th...