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

Real-analytic geodesics in the Mabuchi space of K\"ahler metrics and quantization