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We show that normalized currents of integration along the common zeros ofrandom $m$-tuples of sections of powers of $m$ singular Hermitian big linebundles on a compact K\"ahler manifold distribute asymptotically to the wedgeproduct of the curvature currents of the metrics. If the Hermitian metrics areH\"older with singularities we also estimate the speed of convergence.

H\"older singular metrics on big line bundles and equidistribution