Fairly old app note from ON Semiconductors on using capacitors to drive LEDs off AC mains. Link here (PDF)
This application note describes the basics for powering high current light emitting diodes (LEDs) utilizing a capacitive divider circuit off the AC mains. A linear regulator is used to control the LED current in order to ensure optimal performance and long life. LED characteristics are explained, followed by an example design to illustrate the concept.