## Meaning of connected part / cumulant expectation in physics, algebraic geometry and random matrix literature

I have seen more than once the following notation in algebraic geometry or physics papers: $$\langle tr \frac{1}{M-x_1} \ldots tr \frac{1}{M-x_k} \rangle_c$$ where the angle brackets stand for expectation with respect to some measure (typically given by a Hamiltonian) on the space of matrices $M$, and the author also mentions that the subscript $c$ stands for the connected part of cumulant.I am always puzzled by this last remark. Can anyone point me to the relevant place that explains carefully what the subscript $c$ means in actual computation? I sorta know what cumulant means, but why does it have to do with connected part?

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It'd be nice if you provide examples of places where this appears. I have no idea what it's doing in algebraic geometry. In physics, it is common to compute expectation values using a sum over Feynman diagrams. In such cases "connected" mean we consider the same sum but restrict to connected diagrams – Squark Feb 18 2012 at 13:12