The paper proves equidistribution of preimages of curves for generic finitely supported random walks of the Cremona group on the inverse limit of spaces of currents across models of the plane.
II, In Mod- ern methods in complex analysis, Princeton University Press137(1992), 135–182
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Random products of birational maps: Equidistribution of preimages of curves
The paper proves equidistribution of preimages of curves for generic finitely supported random walks of the Cremona group on the inverse limit of spaces of currents across models of the plane.