Third cumulant of the total transmission of diffuse waves

The probability distribution of the total transmission is studied for waves multiply scattered from a random, static configuration of scatterers. A theoretical study of the second and third cumulants of this distribution is presented. Within a diagrammatic approach a theory is developed that relates the third cumulant normalized to the average, 〈〈${\mathit{T}}_{\mathit{a}}^3$〉〉 to the normalized second cumulant 〈〈${\mathit{T}}_{\mathit{a}}^2$〉〉. For a broad Gaussian beam profile, it is found that 〈〈${\mathit{T}}_{\mathit{a}}^3$〉〉=16/3〈〈${\mathit{T}}_{\mathit{a}}^2$〉${\mathrm{〉}}^2$. This is in good agreement with data of optical experiments.