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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