Wednesday, February 16, 2022 - 09:00 in ZOOM - Video Conference
Loop equations for the classical $\beta$ ensembles: high and low temperature limits
A talk in the Seminar Zufallsmatrizen series by
Peter Forrester from Melbourne University
| Abstract: |
In the context of loop equations, expansions in 1/N are most fami-
liar. But it’s also possible to perform a scaled high temperature ex-
pansion, in which $\beta$ is proportional to 1/N, and a low temperature
expansion in which N is fixed and 1/$\beta$ is the expansion variable. In
fact, there’s a duality between these two expansions. This can be
traced back to functional equations for the moments of the cor-
responding densities. We show that the functional equation can
be extended to the mixed moments, and in fact follows from a
symmetry of the loop equations for the classical $\beta$ ensembles.
Please contact Anas Rahman (anas.rahman@unimelb.edu.au) for details regarding access.
Within the CRC this talk is associated to the project(s): C6 |
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