  The random superposition of many weak sources will produce a stochastic
background of gravitational waves that may dominate the response of the LISA
(Laser Interferometer Space Antenna) gravitational wave observatory. Unless
something can be done to distinguish between a stochastic background and
detector noise, the two will combine to form an effective noise floor for the
detector. Two methods have been proposed to solve this problem. The first is to
cross-correlate the output of two independent interferometers. The second is an
ingenious scheme for monitoring the instrument noise by operating LISA as a
Sagnac interferometer. Here we derive the optimal orbital alignment for
cross-correlating a pair of LISA detectors, and provide the first analytic
derivation of the Sagnac sensitivity curve.
