  Spin excitation spectrum is studied in the double-exchange model with
randomness. Applying the spin wave approximation and the spectral function
analysis, we examine excitation energy and linewidth using analytical as well
as numerical methods. For small wave number $q \sim 0$, the excitation energy
is cosine-like and the linewidth shows a $q$-linear behavior. This indicates
that the spin excitation becomes incoherent or localized near $q = 0$.
Crossover takes place to marginally-coherent regime where both the excitation
energy and the linewidth are proportional to $q^2$. The incoherence is due to
local fluctuations of the kinetic energy of electrons. Comparison with
experimental results in colossal magnetoresistance manganites suggests that
spatially-correlated or mesoscopic-scale fluctuations are more important in
real compounds than local or atomic-scale ones.
