Weakenings and redshifts induced by random propagation times

The crossing by light of a turbulent medium results in a random propagation time. We show that the broadening of monochromatic sources leads to a redshift for a part of the transmitted wave and a spreading for the other part. Gaussian shaped spectra and Gaussian propagation times allow to perform computations about the properties of the received wave. In particular, when it is possible to give a strong enough random character to the propagation, the shift parameter z can reach a sizeable amount, taking smooth hypotheses about the parameters of used Gaussian.