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.
Arithmetic degrees of special cycles and derivatives of Siegel Eisenstein series
Computing the Canonical Height of a Point in Projective Space
Nonarchimedean Green functions and dynamics on projective space
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