Consider the random variable:
area under a lattice walk in the plane from the origin to (n,n) never going
above the diagonal (given by the q-Catalan numbers
2
The mean is:, -1/2 n + 1/2 n
3
The variance is:, -1/6 n + 1/6 n
The asympotics to order 1, of the even alpha coefficients (the (2r)-th momen\
t about the mean divided by the r-th power of the variance)
as an expression in n and r is:
/ 3 r (r - 1)\
(2 r)! |1 - -----------|
\ 10 n /
------------------------
r
r! 2
the (normalized) odd moments, to order 1, are
0
In particular it is asymptotically normal, but we have an even finer asympo\
tics for the alpha coefficients.
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