Characteristic angular scales in cosmic microwave background radiation

We investigate the stochasticity in temperature fluctuations in the cosmic microwave background (CMB) radiation data from the Wilkinson Microwave Anisotropy Probe. We show that the angular fluctuation of the temperature is a Markov process with a Markov angular scale, ΘMarkov = 1.01-0.07+0.09. We characterize the complexity of the CMB fluctuations by means of a Fokker–Planck or Langevin equation and measure the associated Kramers–Moyal coefficients for the fluctuating temperature field T(\ n) and its increment, \Δ T=T(\ n_1)-T(\ n_2) . Through this method we show that temperature fluctuations in the CMB have fat tails compared to a Gaussian distribution.