# Convergence of Siegel–Veech constants

@article{Dozier2016ConvergenceOS, title={Convergence of Siegel–Veech constants}, author={Benjamin Dozier}, journal={Geometriae Dedicata}, year={2016}, volume={198}, pages={131-142} }

We show that for any weakly convergent sequence of ergodic $$SL_2(\mathbb {R})$$SL2(R)-invariant probability measures on a stratum of unit-area translation surfaces, the corresponding Siegel–Veech constants converge to the Siegel–Veech constant of the limit measure. Together with a measure equidistribution result due to Eskin–Mirzakhani–Mohammadi, this yields the (previously conjectured) convergence of sequences of Siegel–Veech constants associated to Teichmüller curves in genus two. The proof…

## 6 Citations

### Equidistribution of saddle connections on translation surfaces

- MathematicsJournal of Modern Dynamics
- 2019

Fix a translation surface $X$, and consider the measures on $X$ coming from averaging the uniform measures on all the saddle connections of length at most $R$. Then as $R\to\infty$, the weak limit of…

### Pairs of saddle connections of typical flat surfaces on fixed affine orbifolds

- Mathematics
- 2022

We prove that the asymptotic number of pairs of saddle connections with length smaller than L with bounded virtual area is quadratic for almost every translation surface with respect to any ergodic…

### Semiclassical Entropy of BPS States in 4d $\mathcal{N}=2$ Theories and Counts of Geodesics

- Mathematics
- 2019

We relate a number of results in the theory of flat surfaces to BPS spectra of a class of 4d $\mathcal{N}=2$ supersymmetric quantum field theories arising from M5 branes wrapped on Riemann surfaces…

### UNIFORM DISTRIBUTION OF SADDLE CONNECTION LENGTHS

- Mathematics
- 2019

For any SL(2,R) invariant and ergodic probability measure on any stratum of flat surfaces, almost every flat surface has the property that its nondecreasing sequence of saddle connection lengths is…

### Semiclassical Entropy of BPS States in 4d N = 2 Theories and Counts of Geodesics

- Mathematics
- 2019

We relate a number of results in the theory of flat surfaces to BPS spectra of a class of 4d N = 2 supersymmetric quantum field theories arising from M5 branes wrapped on Riemann surfaces – A1 class…

### A ug 2 01 8 Uniform distribution of saddle connection lengths

- 2018

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