Explore the fascinating world of random power series with stationary Gaussian coefficients in this 49-minute lecture by Tomoyuki Shirai from Kyushu University, presented at the Institut des Hautes Etudes Scientifiques (IHES). Delve into the properties of zeros in analytic Gaussian processes, comparing them to the i.i.d. coefficients case. Examine the expected number of zeros in a disk and its asymptotic behavior as the radius approaches the convergence limit. Investigate the relationship between zero intensity and spectral density, focusing on cases with well-behaved spectral density functions. Gain insights into this natural generalization of the determinantal point process associated with the Bergman kernel, expanding your understanding of complex analysis and probability theory.