Despite significant progress over more than 100 years, no accelerator has been unambiguously identified as the source of the locally measured flux of cosmic rays. High-energy electrons and positrons are of particular importance in the search for nearby sources as radiative energy losses constrain their propagation to distances of about 1 kpc around 1 TeV. At the highest energies, the spectrum is therefore dominated and shaped by only a few sources whose properties can be inferred from the fine structure of the spectrum at energies currently accessed by experiments like AMS-02, CALET, DAMPE, Fermi-LAT, H.E.S.S. and ISS-CREAM. We present a stochastic model of the Galactic all-electron flux and evaluate its compatibility with the measurement recently presented by the H.E.S.S. collaboration. To this end, we have MC generated a large sample of the all-electron flux from an ensemble of random distributions of sources. We confirm the non-Gaussian nature of the probability density of fluxes at individual energies previously reported in analytical computations. For the first time, we also consider the correlations between the fluxes at different energies, treating the binned spectrum as a random vector and parametrising its joint distribution with the help of a pair-copula construction. We show that the spectral break observed in the all-electron spectrum by H.E.S.S. and DAMPE is statistically compatible with a distribution of astrophysical sources like supernova remnants or pulsars, but requires a rate smaller than the canonical supernova rate. This important result provides an astrophysical interpretation of the spectrum at TeV energies and allows differentiating astrophysical source models from exotic explanations, like dark matter annihilation. We also critically assess the reliability of using catalogues of known sources to model the electron-positron flux.
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