Summary: Lattice paths and orthogonal polynomials: a case
study
Michael Anshelevich
April 13, 2007
PLAN.
· Formulation of the problem: free Meixner polynomials and their free cumu-
lants.
· General orthogonal polynomials.
· Motzkin paths and moments.
· Modified Motzkin model for the free Meixner polynomials.
· Multivariate case: operators.
· Operators on Fock spaces.
1
FORMULATION OF THE PROBLEM.
µt = probability measure on R, mean zero, variance t:
m1(µt) = µt(x) =
R
x dµt(x) = 0,
m2(µt) = µt(x2
) =

Source: Anshelevich, Michael - Department of Mathematics, Texas A&M University

Collections: Mathematics