Search

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

A two-parameter Ehrenfest urn model is derived according to the approach taken by Karlin and McGregor [7] where Krawtchouk polynomials are used. Furthermore, formulas for the mean passage times of finite homogeneous Markov chains with general tridiagonal transition matrices are given. In the special case of the Ehrenfest model they have quite a different structure as compared with those of Blom [2] or Kemperman [9].

Search Results

Refine search

Refine search

Actions for selected content:

2 results

A natural derivative on [0, n] and a binomialPoincaré inequality

Mean passage times for tridiagonal transition matrices and a two-parameter ehrenfest urn model

Search Results

Refine search

Refine search

Actions for selected content:

Save Search

2 results

A natural derivative on [0, n] and a binomialPoincaré inequality

Mean passage times for tridiagonal transition matrices and a two-parameter ehrenfest urn model