Random products of birational maps: Equidistribution of preimages of curves

TL;DR

This paper studies the behavior of preimages of curves under random compositions of birational maps of the plane, demonstrating equidistribution results for generic random walks.

Contribution

It extends the understanding of the Cremona group's action on inverse limits of currents, providing new equidistribution results for random birational transformations.

Findings

Proves equidistribution of preimages for generic finitely supported random walks.

Analyzes the Cremona group's action on inverse limits of currents.

Builds on recent work by Diller and Roeder.

Abstract

We consider iterated preimages of curves by random products of birational transformations of the plane. Following a recent work of Diller and Roeder, we study the action of the Cremona group on the inverse limit of the spaces of currents in all models of the plane. We show equidistribution for generic finitely supported random walks.