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# Equidistribution in Stochastic Dynamical Systems

**Title:** Equidistribution in Stochastic Dynamical Systems

**Speaker: **Bella Tobin (Oregon State University)

**Time: **10:30-11:30 Beijing time, Nov 08, 2022

**Venue:** BIMSA 1118

**Zoom ID:** 293 812 9202 **Passcode: **BIMSA

**Abstract:**

In arithmetic dynamics, one typically studies the behavior and arithmetic properties of a rational map under iteration. Instead of iterating a single rational map, we will consider a countable family of rational maps, iterated according to some probability measure. We call such a system a stochastic dynamical system. As such a family can be infinite and may not be defined over a single number field, we introduce the concept of a generalized adelic measure, generalizing previous notions introduced by Favre and Rivera-Letelier and Mavraki and Ye. Generalized adelic measures are defined over the measure space of places of an algebraic closure of the rational numbers using the framework established by Allcock and Vaaler. This turns heights from sums into integrals. We prove an equidistribution result for generalized adelic measures, and in turn prove an equidistribution theorem for random backwards orbits for stochastic dynamical systems. This talk will include some background in arithmetic dynamics and will be suitable for graduate students.