• Corpus ID: 239024718

On asymptotic behavior of iterates of piecewise constant monotone maps

  title={On asymptotic behavior of iterates of piecewise constant monotone maps},
  author={Konstantin M. Khanin and Liying Li},
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… 
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