# Questions tagged [cumulants]

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### What did Rota mean by "one can define cumulants relative to any sequence of binomial type"?

This question is cross-posted from MSE.$\newcommand{\E}{\mathbb{E}}$ Near the end of "Finite Operator Calculus" (1976), G.C. Rota writes: Note that one can define cumulants relative to any ...
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### Cumulants as coefficients of degree-n polynomial and conditions for real roots

In a $(n-1)$-degree polynomial, $P_{n-1}(z) = c_{n-1} z^{n-1} + c_{n-2} z^{n-2} + \ldots + c_0$, defined by, P_{n-1}(z) = \sum\limits_{i=1}^n \, \prod\limits_{j=1,j\neq i}^n (z-x_j) \...
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### 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 ...
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### 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 ...
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