# Concentration of solutions to random equations with concentration of measure hypotheses

@article{Louart2020ConcentrationOS, title={Concentration of solutions to random equations with concentration of measure hypotheses}, author={Cosme Louart and Romain Couillet}, journal={arXiv: Probability}, year={2020} }

We propose here to study the concentration of random objects that are implicitly formulated as fixed points to equations Y = f (X) where f is a random mapping. Starting from an hypothesis taken from the concentration of the measure theory, we are able to express precisely the concentration of such solutions, under some contractivity hypothesis on f. This statement has important implication to random matrix theory, and is at the basis of the study of some optimization procedures like the…

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