In several naturally occurring (infinite) point processes, the number the points inside a finite domain can be determined, almost surely, by the point configuration outside the domain.

# Ergodic Theory & Statistical Mechanics

This weekly seminar welcomes many visiting speakers and also provides a forum for results by Princeton/IAS faculty and graduate students. While most talks focus on one of the two namesake topics, there tends to be overlap with other fields. Most recently, talks have included material on celestial mechanics, number theory, probability theory, the Schrodinger equation, spectral theory and Teichmueller theory.

For more information about this seminar, contact Yakov Sinai or Jon Fickenscher

**Please click on seminar title for complete abstract.**

##### Rigidity phenomena in random point sets and applications

Princeton University

##### Higher Rank Orbit Closures in Genus 3

The moduli space of translation surfaces is stratified by the orders of the zeros of Abelian differentials.

University of Chicago

##### Randomization of initial data and global well-posedness

**Please note special day (Friday) and location. ** In this talk, we will present techniques of randomization to get global well-posedness on sets of initial data with non zero measure, the measure being related to the randomization.

Universit´e Paris 13, CNRS

##### Outer billiards and the plaid model

Outer billiards is a billiards-like dynamical system which is defined on the outside of a convex shape in the plane. Even for simple shapes, like kites (bilaterally symmetric quadrilaterals), the orbits have an intricate fractal-like structure.

Brown University