• Corpus ID: 239024718

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… 
Point Fields of Last Passage Percolation and Coalescing Fractional Brownian Motions
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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