5 research outputs found
Correlation Functions of Harish-Chandra Integrals over the Orthogonal and the Symplectic Groups
The Harish-Chandra correlation functions, i.e. integrals over compact groups
of invariant monomials prod tr{X^{p_1} Omega Y^{q_1} Omega^dagger X^{p_2} ...
with the weight exp tr{X Omega Y Omega^dagger} are computed for the orthogonal
and symplectic groups. We proceed in two steps. First, the integral over the
compact group is recast into a Gaussian integral over strictly upper triangular
complex matrices (with some additional symmetries), supplemented by a summation
over the Weyl group. This result follows from the study of loop equations in an
associated two-matrix integral and may be viewed as the adequate version of
Duistermaat-Heckman's theorem for our correlation function integrals. Secondly,
the Gaussian integration over triangular matrices is carried out and leads to
compact determinantal expressions.Comment: 58 pages; Acknowledgements added; small corrections in appendix A;
minor changes & Note Adde
A Matrix model for plane partitions
We construct a matrix model equivalent (exactly, not asymptotically), to the
random plane partition model, with almost arbitrary boundary conditions.
Equivalently, it is also a random matrix model for a TASEP-like process with
arbitrary boundary conditions. Using the known solution of matrix models, this
method allows to find the large size asymptotic expansion of plane partitions,
to ALL orders. It also allows to describe several universal regimes.Comment: Latex, 41 figures. Misprints and corrections. Changing the term TASEP
to self avoiding particle porces
Correlation Functions of Harish-Chandra Integrals over the Orthogonal and the Symplectic Groups
58 pagesThe Harish-Chandra correlation functions, i.e. integrals over compact groups of invariant monomials prod tr{X^{p_1} Omega Y^{q_1} Omega^dagger X^{p_2} ... with the weight exp tr{X Omega Y Omega^dagger} are computed for the orthogonal and symplectic groups. We proceed in two steps. First, the integral over the compact group is recast into a Gaussian integral over strictly upper triangular complex matrices (with some additional symmetries), supplemented by a summation over the Weyl group. This result follows from the study of loop equations in an associated two-matrix integral and may be viewed as the adequate version of Duistermaat-Heckman's theorem for our correlation function integrals. Secondly, the Gaussian integration over triangular matrices is carried out and leads to compact determinantal expressions