This paper presents the experimental results of a cumulant analysis of
the extended x-ray absorption fine structure amplitude of GaAs at the
K edges of Ga and As. The second and fourth cumulants of the distance
distributions of the near neighbours of Ga and As have been obtained
as a function of temperature in the range 77-450 K. The fourth cumulan
t of Ga-As nearest-neighbour distance distributions is zero in the exa
mined temperature range; a non-Gaussian distribution of the second and
third coordination shell distances of Ga and As has been revealed for
the first time. Temperature dependences of mean square relative displ
acements (MSRDS) of the first three shells of Ga and As have been comp
ared with Einstein and correlated Debye models. The MSRD of the first-
shell Ga-As distance is connected to the optical modes at 7.6-8 THz of
the phonon spectrum of GaAs.