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We prove a joint partial equidistribution result for common perpendicularswith given density on equidistributing equidistant hypersurfaces, towards ameasure supported on truncated stable leaves. We recover a result of Marklof onthe joint partial equidistribution of Farey fractions at a given density, andgive several analogous arithmetic applications, including in Bruhat-Tits trees.

Joint partial equidistribution of Farey rays in negatively curved manifolds and trees