A Generalisation of Dyson's Integration Theorem for Determinants
Akemann, Gernot
Akemann
Gernot
Shifrin, Leonid
Shifrin
Leonid
Dyson's integration theorem is widely used in the computation of eigenvaluecorrelation functions in Random Matrix Theory. Here we focus on the variant ofthe theorem for determinants, relevant for the unitary ensembles with Dysonindex beta = 2. We derive a formula reducing the (n-k)-fold integral of an n xn determinant of a kernel of two sets of arbitrary functions to a determinantof size k x k. Our generalisation allows for sets of functions that are notorthogonal or bi-orthogonal with respect to the integration measure. In thespecial case of orthogonal functions Dyson's theorem is recovered.
40
32
F785-F791
F785-F791
IOP Publishing
2007