The partition function of Beta-ensembles with complex potentials
A talk in the Seminar Zufallsmatrizen series by
Alex Little
| Abstract: | A Beta-ensemble can be viewed as a gas of particles confined to a line with logarithmic pairwise interactions and at inverse temperature Beta. The partition function of a Beta-ensemble involves a large parameter N which appears both in the integrand and as the number of integrations, and thus its asymptotic analysis could be regarded as an infinite-dimensional version of the Laplace method. In joint work with A. Guionnet and K. Kozlowski, we consider the partition function of a Beta-ensemble with a complex-valued potential. We prove, under certain hypotheses, a full 1/N expansion of this partition function and explicitly identify the first few terms. Because the integrand is complex, and hence oscillatory, our method could be regarded as an infinite-dimensional version of the Steepest Descent method. ArXiv reference: https://arxiv.org/abs/2411.10610 Within the CRC this talk is associated to the project(s): C6 |