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

Part of: Ergodic theory Arithmetic and non-Archimedean dynamical systems Arithmetic algebraic geometry

Published online by Cambridge University Press:  26 February 2021

WADE HINDES
WADE HINDES*
Affiliation:
Department of Mathematics, Texas State University, 601 University Dr., San Marcos, TX78666, U.S.A. e-mail: [email protected]
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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.

MSC classification

Primary: 37P15: Global ground fields 37A50: Relations with probability theory and stochastic processes
Secondary: 11G50: Heights
Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 171 , Issue 2 , September 2021 , pp. 369 - 385
Copyright
© The Author(s), 2021. Published by Cambridge University Press on behalf of Cambridge Philosophical Society

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References

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