Summary: Free Brownian motion
Michael Anshelevich
Texas A&M University
October 8, 2009
Michael Anshelevich Free Brownian motion
Definition I: Combinatorics.
Catalan numbers
ck =
1
k + 1
2k
k
: 1, 1, 2, 5, 14, . . .
Count many things (Stanley Exercise 6.19(a-nnn) +109).
Count lattice paths: , , ,
, , , ,
How many with k steps?
m2k+1 = 0.
m2k = ck = Catalan number.
Michael Anshelevich Free Brownian motion

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

Collections: Mathematics