Counting Problems for Invariant Point Processes

Jayadev S. Athreya ()
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Jayadev S. Athreya: University of Washington, Department of Mathematics

Chapter Chapter 10 in In the Tradition of Thurston III, 2024, pp 339-363 from Springer

Abstract: Abstract Using linear algebra and the ergodic theory of SL ( 2 , ℝ ) $$\mathrm {SL}(2,\mathbb {R})$$ actions, we survey how to solve several natural asymptotic counting problems for discrete subsets of the plane using an axiomatic perspective. Applications include counting holonomies of saddle connections, lattice points, and fine scale distribution in various contexts. This is a perspective inspired by work of Veech (Ann. Math. (2) 148(3):895–944, 1998), and developed further by, among others, Eskin–Masur (Ergodic Theory Dyn. Syst. 21(2):443–478, 2001), Athreya–Ghosh (Enseign. Math. 64(1–2), 1–21, 2018), and Marklof (Lond. Math. Soc. Newsl. 493:42–49, 2021).

Keywords: Point process; Saddle connection; Random lattice; Poisson process; 60G55; 32G15; 11H60 (search for similar items in EconPapers)
Date: 2024
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-031-43502-7_10

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DOI: 10.1007/978-3-031-43502-7_10

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