Thursday, May 23, 2019 - 16:15 in D5-153
Critical behaviour and characteristic polynomials of non-Hermitian random matrices
A talk in the Kolloquium Mathematische Physik series by
Nicholas Simm
| Abstract: |
I will discuss some recent developments regarding the normal matrix model. In particular my interest will be in certain critical models where the limiting support of the eigenvalues can radically change its topology by slightly adjusting an external parameter. I will discuss how aspects of the model can be explicitly mapped to the study of expectations of characteristic polynomials of non-Hermitian random matrices (e.g. Ginibre or truncated unitary). Many of these averages are related to Painlev transcendents, and by exploiting this, a precise and non-trivial asymptotic expansion of partition functions can be calculated in the critical models. This is joint work with Alfredo Deao (University of Kent).
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