The asymptotic bootstrap method and Continued Fractions
Speaker
David Berenstein
Affiliation
University of California, Santa Barbara
Abstract
I will explain a baby model of a bootstrap problem where one can prove convergence to the right answer. The model looks to find high precision solutions to a moment problem or a Fourier moment problem. I will explain why this problem needs to be solved to very high precision in order to be applied to Matrix models of a single matrix (there are two types of matrix models under consideration, Unitary matrix models and Hermitian matrix models and two associated baby models).
David Berenstein
Affiliation
University of California, Santa Barbara
Abstract
I will explain a baby model of a bootstrap problem where one can prove convergence to the right answer. The model looks to find high precision solutions to a moment problem or a Fourier moment problem. I will explain why this problem needs to be solved to very high precision in order to be applied to Matrix models of a single matrix (there are two types of matrix models under consideration, Unitary matrix models and Hermitian matrix models and two associated baby models).
The original problem is based on positivity of a measure and I will describe how that version implies a different way of looking at the problem that can be moved to the complex plane. At this point, in the simplest setup one finds that the model predicts a solution expressed as a continuous fraction. I will describe some of the convergence properties of the continued fraction as well as how the continued fraction is an analytic function that provides a non-perturbative completion of an asymptotic series and I will also explain some generalizations of this problem. Finally, I will show numerical applications these techniques to matrix models.