On asymptotic behavior of iterates of piecewise constant monotone maps

Konstantin Khanin; Liying Li

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arXiv · 2110.09731

On asymptotic behavior of iterates of piecewise constant monotone maps

Konstantin Khanin·Liying Li

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Abstract

In this paper we study the rate of convergence of the iterates of \iid random piecewise constant monotone maps to the time-$1$ transport map for the process of coalescing Brownian motions. We prove that the rate of convergence is given by a power law. The time-1 map for the coalescing Brownian motions can be viewed as a fixed point for a natural renormalization transformation acting in the space of probability laws for random piecewise constant monotone maps. Our result implies that this fixed point is exponentially stable.

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Konstantin Khanin, Liying Li. 2021-10-19. On asymptotic behavior of iterates of piecewise constant monotone maps. https://arxiv.org/abs/2110.09731

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