References of "Johnson, Oliver"
     in
Bookmark and Share    
Full Text
Peer Reviewed
See detailDiscrete versions of the transport equation and the Shepp-Olkin conjecture
Hillion, Erwan UL; Johnson, Oliver

in Annals of Probability (2016), 44(1), 276-306

We introduce a framework to consider transport problems for integer-valued random variables. We introduce weighting coeffcients which allow us to characterise transport problems in a gradient now setting ... [more ▼]

We introduce a framework to consider transport problems for integer-valued random variables. We introduce weighting coeffcients which allow us to characterise transport problems in a gradient now setting, and form the basis of our introduction of a discrete version of the Benamou--Brenier formula. Further, we use these coeffcients to state a new form of weighted log-concavity. These results are applied to prove the monotone case of the Shepp--Olkin entropy concavity conjecture. [less ▲]

Detailed reference viewed: 112 (9 UL)
Full Text
Peer Reviewed
See detailA natural derivative on [0, n] and a binomial Poincaré inequality
Hillion, Erwan UL; Johnson, Oliver; Yu, Yaming

in ESAIM: Probability and Statistics = Probabilité et statistique : P & S (2014), 18

We consider probability measures supported on a finite discrete interval [0, n]. We introduce a new finite difference operator ∇n, defined as a linear combination of left and right finite differences. We ... [more ▼]

We consider probability measures supported on a finite discrete interval [0, n]. We introduce a new finite difference operator ∇n, defined as a linear combination of left and right finite differences. We show that this operator ∇n plays a key role in a new Poincaré (spectral gap) inequality with respect to binomial weights, with the orthogonal Krawtchouk polynomials acting as eigenfunctions of the relevant operator. We briefly discuss the relationship of this operator to the problem of optimal transport of probability measures. [less ▲]

Detailed reference viewed: 68 (1 UL)