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5
votes
0answers
71 views

Joint cumulants of $Z_2^n$ characters

Let $f_{c}:Z_2^n \rightarrow \{-1,1\}$ be the character defined as $f_c(x) = (-1)^{<x,c>}$, where $c,x \in Z_2^n$. It is easy to see that since $f_{c_1}\cdot\ldots\cdot f_{c_k} = f_{c_1 \oplus ...
2
votes
0answers
219 views

Is connected correlation/cumulant expansion additive?

Say X is a free field or a Gaussian random variable. Then I want to analyse the connected correlation, $<(X + a (X^2 - \langle X^2 \rangle))^n>_c$ I think that for $n \geq 4$ there are no ...
5
votes
1answer
371 views

cumulant problem

A couple of days after I posted this to stackexchange, no one's answered: I take the problem of cumulants to be this: given a sequence $(\kappa_1,\kappa_2,\kappa_3,\ldots)$ of real numbers, is it the ...
1
vote
0answers
312 views

Generalizations of Gram-Charlier and Edgeworth series?

I am looking for references pertaining to, and/or help in deriving, generalizations of the Gram-Charlier and Edgeworth series for non-Gaussian reference probability distributions. I would like to ...