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We show that normalized currents of integration along the common zeros of random   $m$  -tuples of sections of powers of   $m$   singular Hermitian big line bundles on a compact Kähler manifold distribute asymptotically to the wedge product of the curvature currents of the metrics. If the Hermitian metrics are Hölder with singularities we also estimate the speed of convergence.

Hölder Singular Metrics on Big Line Bundles and Equidistribution