On asymptotic behavior of iterates of piecewise constant monotone maps
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 time1 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.
 Publication:

arXiv eprints
 Pub Date:
 October 2021
 arXiv:
 arXiv:2110.09731
 Bibcode:
 2021arXiv211009731K
 Keywords:

 Mathematics  Probability;
 60J65;
 60J05;
 37H30;
 37A25