Systems and methods for independently managing wireless transmission by individual spectrum access systems in a radio frequency spectrum shared by a plurality of spectrum access systems. An example method includes: receiving, by the spectrum access system, an interference budget from a sensor; determining, by the spectrum access system, secondary users managed by the spectrum access system in a radio frequency spectrum shared by a plurality of spectrum access systems; managing a move list for the spectrum access system independently of the other spectrum access systems in an absence of exchange of spectrum grant information with the other spectrum access systems; and determining the move list for the spectrum access system from a first moment and a second moment of an aggregate interference distribution such that the spectrum access system provides grants to its secondary users in a dynamic protection area of the spectrum access system.