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The search of a clustering signal in the arrival directions ofultra-high-energy cosmic rays (UHECRs) is a standard method to assess the levelof anisotropy of the data sets under investigation. Here, we first show how toquantify the sensitivity of a UHECR detector to the detection of anisotropy,and then propose a new method that pushes forward the study of the two-pointauto-correlation function, enabling one to put astrophysically meaningfulconstraints on both the effective UHECR source density and the angulardeflections that these charged particles suffer while they propagate throughthe galactic and intergalactic magnetic fields. We apply the method tosimulated data sets obtained under various astrophysical conditions, and showhow the input model parameters can be estimated through our analysis,introducing the notion of "clustering similarity" (between data sets), to whichwe give a precise statistical meaning. We also study how the constraining powerof the method is influenced by the size of the data set under investigation,the minimum energy of the UHECRs to which it is applied, and a prior assumptionabout the underlying source distribution. We also show that this method isparticularly adapted to data sets consisting of a few tens to a few hundreds ofevents, which corresponds to the current and near-future observationalsituation in the field of UHECRs.

Extended clustering analyses to constrain the deflection angular scale and source density of the ultra-high-energy cosmic rays