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We provide conditions that guarantee local rates of convergence indistribution of iterated random functions that are not nonexpansive mappings inlocally compact Hadamard spaces. Our results are applied to stochasticinstances of common algorithms in optimization, stochastic tomography for X-FELimaging, and a stochastic algorithm for the computation of Fr\'echet means inmodel spaces for phylogenetic trees.

Rates of Convergence for Chains of Expansive Markov Operators