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The small-scale distribution of dark matter in Galactic halos is poorlyknown. Several studies suggest that it could be very clumpy, which turns out tobe of paramount importance when investigating the annihilation signal fromexotic particles (e.g. supersymmetric or Kaluza-Klein). In this paper we focuson the annihilation signal in positrons. We estimate the associateduncertainty, due to the fact that we do not know exactly how the clumps aredistributed in the Galactic halo. To this aim, we perform a statistical studybased on analytical computations, as well as numerical simulations. Inparticular, we study the average and variance of the annihilation signal overmany Galactic halos having the same statistical properties. We find that theso-called boost factor used by many authors should be handled with care, as i)it depends on energy and ii) it may be different for positrons, antiprotons andgamma rays, a fact which has not received any attention before. As anillustration, we use our results to discuss the positron spectrum measurementsby the HEAT experiment.Comment: 31 pages, 12 figures, accepted in A&

Clumpiness of dark matter and the positron annihilation signal