Orthogonal Transition Kernels

Wavelets by orthogonal rational kernels

Suppose f k g n k=0 is an orthonornal basis for the function space L n of polynomi-als or rational functions of degree n with prescribed poles. Suppose n = 2 s and set V s = L n. Then k n (z; w) = P n k=0 k (z) k (w), is a reproducing kernel for V s. For xed w, such reproducing kernels are known to be functions localized in the neighborhood of z = w. Moreover, by an appropriate choice of the pa...

Optimal measures and transition kernels

Optimal measures and Markov transition kernels ∗ Roman

We study optimal solutions to an abstract optimization problem for measures, which is a generalization of classical variational problems in information theory and statistical physics. In the classical problems, information and relative entropy are defined using the Kullback-Leibler divergence, and for this reason optimal measures belong to a oneparameter exponential family. Measures within such...

Optimal measures and Markov transition kernels

We study optimal solutions to an abstract optimization problem for measures, which is a generalization of classical variational problems in information theory and statistical physics. In the classical problems, information and relative entropy are defined using the Kullback-Leibler divergence, and for this reason optimal measures belong to a oneparameter exponential family. Measures within such...

Correlation Kernels for Discrete Symplectic and Orthogonal Ensembles

In [41] H. Widom derived formulae expressing correlation functions of orthogonal and symplectic ensembles of random matrices in terms of orthogonal polyno-mials. We obtain similar results for discrete ensembles with rational discrete logarithmic derivative, and compute explicitly correlation kernels associated to the classical Meixner and Charlier weights.