# Dynamical and arithmetic degrees for random iterations of maps on projective space

## TL;DR

This paper proves that the dynamical degree of a random sequence of rational maps on projective space is almost surely constant and explores implications for height growth and counting in random orbits.

## Contribution

It establishes the almost sure constancy of dynamical degrees for i.i.d. random rational maps and applies this to height-related problems in dynamics.

## Key findings

- Dynamical degree is almost surely constant for i.i.d. random maps.
- Application to height growth in random orbits.
- Results on height counting in the context of random dynamics.

## Abstract

We show that the dynamical degree of an (i.i.d) random sequence of dominant, rational self-maps on projective space is almost surely constant. We then apply this result to height growth and height counting problems in random orbits.