# On asymptotic behavior of iterates of piecewise constant monotone maps

@inproceedings{Khanin2021OnAB, title={On asymptotic behavior of iterates of piecewise constant monotone maps}, author={Konstantin M. Khanin and Liying Li}, year={2021} }

In this paper we study the rate of convergence of the iterates of i.i.d. 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…

## One Citation

Point Fields of Last Passage Percolation and Coalescing Fractional Brownian Motions

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- 2021

We consider large-scale point fields which naturally appear in the context of the Kardar-ParisiZhang (KPZ) phenomenon. Such point fields are geometrical objects formed by points of mass…

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