We study a system of all-to-all weakly coupled uniformly expanding circle
maps in the thermodynamic limit. The state of the system is described by a
probability measure and its evolution is given by the action of a nonlinear
operator, also called a self-consistent transfer operator. We prove that when
the coupling is sufficiently small, the system has a unique stable state that
satisfies a linear response formula when varying the coupling strength.Comment: Electronic copy of final peer-reviewed manuscript accepted for
publicatio