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The flux and nuclear composition of ultra-high energy cosmic rays depend onthe cosmic distribution of their sources. Data from cosmic ray observatoriesare yet inconclusive about their exact location or distribution, but provide ameasure for the average local density of these emitters. Due to thediscreteness of the emitters the flux and nuclear composition is expected toshow ensemble fluctuations on top of the statistical variations, i.e. "cosmicvariance". This effect is strongest for the most energetic cosmic rays due tothe limited propagation distance in the cosmic radiation background and ishence a local phenomenon. For the statistical analysis of cosmic ray emissionmodels it is important to quantify the possible level of this variance. In thispaper we present a completely analytic method that describes the variation ofthe flux and nuclear composition with respect to the local source density. Wehighlight that proposed future space-based observatories with exposures ofO(10^6 km^2 sr yr) will attain sensitivity to observe these spectralfluctuations in the cosmic ray energy spectrum at Earth relative to the overallpower-law fit.

Ensemble Fluctuations of the Flux and Nuclear Composition of Ultra-High Energy Cosmic Ray Nuclei