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The statistical scattering properties of wave transport in disorderedwaveguides are derived perturbatively within the transition matrix formalism.The limiting macroscopic statistic of the wave transport, emerges as aconsequence of a generalized central-limit-theorem: the expectation values ofmacroscopic observables depend only on the first and second moments of thereflection matrix of individual scatterers. This theoretical approach does notconsider any statistical assumption on the scattering properties of theindividual scatterers and it is fully consistent with the optical theorem. Theresults are found in the so called dense-weak-scattering limit and in theballistic regime.

Central limit theorem for the wave transport in disordered waveguides: a perturbative approach