  We examine statistical properties of a laser beam propagating in a turbulent
medium. We prove that the intensity fluctuations at large propagation distances
possess Gaussian probability density function and establish quantitative
criteria for realizing the Gaussian statistics depending on the laser
propagation distance, the laser beam waist, the laser frequency and the
turbulence strength. We calculate explicitly the laser envelope pair
correlation function and corrections to its higher order correlation functions
breaking Gaussianity. We discuss also statistical properties of the brightest
spots in the speckle pattern.
