3 papers
math.NT2020
An exponentially averaged Vasyunin formula
Sébastien Darses, Erwan Hillion
We prove a Vasyunin-type formula for an autocorrelation function arising from a Nyman-Beurling criterion generalized to a probabilistic framework. This formula can also be seen as…
math.PR2018
A proof of the Shepp-Olkin entropy monotonicity conjecture
Erwan Hillion, Oliver Johnson
Consider tossing a collection of coins, each fair or biased towards heads, and take the distribution of the total number of heads that result. It is natural to conjecture that this…
math.PR2018
An extremal property of the normal distribution, with a discrete analog
Erwan Hillion, Oliver Johnson, Adrien Saumard
We prove, using the Brascamp-Lieb inequality, that the Gaussian measure is the only strong log-concave measure having a strong log-concavity parameter equal to its covariance matri…