  We introduce the concept of stationary graviton non-Gaussianity (nG), an
observable that can be probed in terms of 3-point correlation functions of a
stochastic gravitational wave (GW) background. When evaluated in momentum
space, stationary nG corresponds to folded bispectra of graviton nG. We
determine 3-point overlap functions for testing stationary nG with pulsar
timing array GW experiments, and we obtain the corresponding optimal
signal-to-noise ratio. For the first time, we consider 3-point overlap
functions including scalar graviton polarizations (which can be motivated in
theories of modified gravity); moreover, we also calculate 3-point overlap
functions for correlating pulsar timing array with ground based GW detectors.
The value of the optimal signal-to-noise ratio depends on the number and
position of monitored pulsars. We build geometrical quantities characterizing
how such ratio depends on the pulsar system under consideration, and we
evaluate these geometrical parameters using data from the IPTA collaboration.
We quantitatively show how monitoring a large number of pulsars can increase
the signal-to-noise ratio associated with measurements of stationary graviton
nG.
