Accretion disks power some of the most energetic phenomena in the universe—from the formation of planets to the launching of relativistic jets by black holes. A central ingredient in these systems is turbulence, which transports angular momentum and allows matter to spiral inward. The primary engine of this turbulence, the magnetorotational instability (MRI), cannot operate indefinitely unless large-scale magnetic fields are continually regenerated. Understanding how these fields arise has remained an open challenge because dynamo theory and angular-momentum transport have long been studied separately. 

 In this talk, I will present a unified statistical framework that connects these processes using direct statistical simulations (DSS) of MRI turbulence. This approach tracks both mean fields and their correlations, revealing how shear and rotation reorganize turbulent motions to build coherent magnetic structures. Our analysis identifies two key dynamo mechanisms—the rotation–shear–current effect and the rotation–shear–vorticity effect—which naturally generate the large-scale radial and vertical magnetic fields seen in simulations. I will also discuss the role of helicity in structuring turbulent disks and show how these insights lead to improved, physics-based sub-grid models for global accretion-disk simulations, including those used by the Event Horizon Telescope (EHT) collaboration.