6 citations · 6 across the 3 of their papers we have counts for
9 papers
Concentration Inequalities for Ultra Log-Concave Distributions
Heshan Aravinda, Arnaud Marsiglietti, James Melbourne
We establish concentration inequalities in the class of ultra log-concave distributions. In particular, we show that ultra log-concave distributions satisfy Poisson concentration b…
Concentration functions and entropy bounds for discrete log-concave distributions
Sergey G. Bobkov, Arnaud Marsiglietti, James Melbourne
Two-sided bounds are explored for concentration functions and Rényi entropies in the class of discrete log-concave probability distributions. They are used to derive certain varian…
Entropic CLT for smoothed convolutions and associated entropy bounds
Sergey G. Bobkov, Arnaud Marsiglietti
We explore an asymptotic behavior of entropies for sums of independent random variables that are convolved with a small continuous noise.
Local limit theorems for smoothed Bernoulli and other convolutions
Sergey G. Bobkov, Arnaud Marsiglietti
We explore an asymptotic behavior of densities of sums of independent random variables that are convoluted with a small continuous noise.
Further investigations of Rényi entropy power inequalities and an entropic characterization of s-concave densities
Jiange Li, Arnaud Marsiglietti, James Melbourne
We investigate the role of convexity in Rényi entropy power inequalities. After proving that a general Rényi entropy power inequality in the style of Bobkov-Chistyakov (2015) fails…
Asymptotic behavior of Rényi entropy in the central limit theorem
Sergey G. Bobkov, Arnaud Marsiglietti
We explore an asymptotic behavior of Rényi entropy along convolutions in the central limit theorem with respect to the increasing number of i.i.d. summands. In particular, the prob…