Concavity of entropy along binomial convolutions
نویسندگان
چکیده
منابع مشابه
Concavity of entropy along binomial convolutions
Motivated by a generalization of Sturm-Lott-Villani theory to discrete spaces and by a conjecture stated by Shepp and Olkin about the entropy of sums of Bernoulli random variables, we prove the concavity in t of the entropy of the convolution of a probability measure a, which has the law of a sum of independent Bernoulli variables, by the binomial measure of parameters n ≥ 1 and t.
متن کاملOn Divisibility of Convolutions of Central Binomial Coefficients
Recently, Z. Sun proved that 2 (2m + 1) ( 2m m ) | ( 6m 3m )( 3m m ) for m ∈ Z>0. In this paper, we consider a generalization of this result by defining bn,k = 2k (n + 2k − 2)!! (n− 2)!! k! . In this notation, Sun’s result may be expressed as 2 (2m + 1) | b(2m+1),(2m+1)−1 for m ∈ Z>0. In this paper, we prove that 2n | bn,un±2r for n ∈ Z>0 and u, r ∈ Z>0 with un ± 2r > 0. In addition, we prove a...
متن کاملThe concavity of Rènyi entropy power
We associate to the p-th Rényi entropy a definition of entropy power, which is the natural extension of Shannon’s entropy power and exhibits a nice behaviour along solutions to the p-nonlinear heat equation in Rn. We show that the Rényi entropy power of general probability densities solving such equations is always a concave function of time, whereas it has a linear behaviour in correspondence ...
متن کاملOn the q - log - Concavity of Gaussian Binomial Coefficients 335
We give a combinatorial proof that k l-k-1 l + t q q q q a polynomial in q with nonnegative coefficients for nonnegative integers a, b, k, lwith a>~b and l~>k. In particular, for a=b=n and l=k, this implies the q-log-concavity of the Gaussian binomial coefficients k , which was conjectured q by BUTLER (Proc.
متن کاملEntropy of Convolutions on the Circle
Given ergodic p-invariant measures f i g on the 1-torus T = R=Z, we give a sharp condition on their entropies, guaranteeing that the entropy of the convolution 1 n converges to log p. We also prove a variant of this result for joinings of full entropy on T N. In conjunction with a method of Host, this yields the following. Denote q (x) = qx (mod 1). Then for every p-invariant ergodic with posit...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Electronic Communications in Probability
سال: 2012
ISSN: 1083-589X
DOI: 10.1214/ecp.v17-1707