Real-analytic geodesics in the Mabuchi space of Kähler metrics and quantization

Abstract: We prove the convergence of quantized Bergman geodesics to the Mabuchi geodesics for the initial value problem, in the case of real-analytic initial data and in short time. This partially solves a conjecture of Y. Rubinstein and the last author. We also argue against the existence of a solution to the boundary value problem, generically in real-analytic regularity.