Multiple orthogonal polynomials of mixed type and non-intersecting Brownian motions

Details Multiple orthogonal polynomials of mixed type and non-intersecting Brownian motions Multiple orthogonal polynomials of mixed type and non-intersecting Brownian motions

2005-11-18

arxiv.org/abs/math/0511470v1

Journal of Approximation Theory 146 (2007), 91--114

Mathematics

Classical Analysis and ODEs

22 pages, 4 figures

Scientific paper

We present a generalization of multiple orthogonal polynomials of type I and type II, which we call multiple orthogonal polynomials of mixed type. Some basic properties are formulated, and a Riemann-Hilbert problem for the multiple orthogonal polynomials of mixed type is given. We derive a Christoffel-Darboux formula for these polynomials using the solution of the Riemann-Hilbert problem. The main motivation for studying these polynomials comes from a model of non-intersecting one-dimensional Brownian motions with a given number of starting points and endpoints. The correlation kernel for the positions of the Brownian paths at any intermediate time coincides with the Christoffel-Darboux kernel for the multiple orthogonal polynomials of mixed type with respect to Gaussian weights.

Affiliated with

Also associated with

No associations

Rating

Multiple orthogonal polynomials of mixed type and non-intersecting Brownian motions does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Multiple orthogonal polynomials of mixed type and non-intersecting Brownian motions, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Multiple orthogonal polynomials of mixed type and non-intersecting Brownian motions will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-710921