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Lattice paths and orthogonal polynomials: a case Michael Anshelevich
 

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.
t = probability measure on R, mean zero, variance t:
m1(t) = t(x) =
R
x dt(x) = 0,
m2(t) = t(x2
) =

  

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

 

Collections: Mathematics