Ursell function

In statistical mechanics, an Ursell function. or connected correlation function, is a cumulant of a random variable in statistical mechanics. It is also called a connected correlation function as it can often be obtained by summing over connected Feynman diagrams (the sum over all Feynman diagrams gives the correlation functions).

If X is a random variable, the moments s_n and cumulants or Ursell functions u_n are given by

$E(\exp(zX)=\sum _{n}s_{n}z^{n}/n!=\exp \left(\sum _{n}u_{n}z^{n}/n!\right)$

(where E is the expectation).

References

• Glimm, James; Jaffe, Arthur (1987), Quantum physics (2nd ed.), Berlin, New York: Springer-Verlag, ISBN 978-0-387-96476-8, MR 0887102