  Signatures of stochastic effects in the radiation of a relativistic electron
beam interacting with a counterpropagating superstrong short focused laser
pulse are investigated in a quantum regime when the electron's radiation
dominates its dynamics. We consider the electron-laser interaction at
near-reflection conditions when pronounced high-energy gamma-ray bursts arise
in the backward-emission direction with respect to the initial motion of the
electrons. The quantum stochastic nature of the gamma-photon emission is
exhibited in the angular distributions of the radiation and explained in an
intuitive picture. Although, the visibility of the stochasticity signatures
depends on the laser and electron beam parameters, the signatures are of a
qualitative nature and robust. The stochasticity, a fundamental quantum
property of photon emission, should thus be measurable rather straightforwardly
with laser technology available in near future.
