  It is argued that the amplitudes of the production of $n$ soft scalar
particles by one or a few energetic ones in theories like $\lambda\phi^4$ has
the exponential form, $A_n\propto\sqrt{n!}\exp[{1\over\lambda}F(\lambda
n,\epsilon)]$, in the regime $\lambda\to 0$, $\lambda n={fixed}$,
$\epsilon={fixed}$, where $\epsilon$ is the typical kinetic energy of outgoing
particles. Existing results support this conjecture. Several new analytical and
numerical results in favor of the exponential behavior of multiparticle
amplitudes are presented.
