8 citations · 23 across the 8 of their papers we have counts for
8 papers
Uniform distribution of saddle connection lengths in all orbits
Donald Robertson, Benjamin Dozier
For every flat surface, almost every flat surface in its orbit has the following property: the sequence of its saddle connection lengths in non-decreasi…
Counting geodesics on expander surfaces
Benjamin Dozier, Jenya Sapir
We study properties of typical closed geodesics on expander surfaces of high genus, i.e. closed hyperbolic surfaces with a uniform spectral gap of the Laplacian. Under an additiona…
Simple vs non-simple loops on random regular graphs
Benjamin Dozier, Jenya Sapir
In this note we solve the ``birthday problem'' for loops on random regular graphs. Namely, for fixed , we prove that on a random -regular graph with vertices, as …
Equations of linear subvarieties of strata of differentials
Frederik Benirschke, Benjamin Dozier, Samuel Grushevsky
For a linear subvariety of a stratum of meromorphic differentials, we investigate its closure in the multi-scale compactification constructed by Bainbridge-Chen-Gendron-Grushev…
Measure bound for translation surfaces with short saddle connections
Benjamin Dozier
We prove that any ergodic -invariant probability measure on a stratum of translation surfaces satisfies strong regularity: the measure of the set of surfaces with two non-…
Coarse density of subsets of
Benjamin Dozier, Jenya Sapir
Let be the moduli space of genus Riemann surfaces. We show that an algebraic subvariety of is coarsely dense with respect to the Teichmüller met…
Equidistribution of saddle connections on translation surfaces
Benjamin Dozier
Fix a translation surface , and consider the measures on coming from averaging the uniform measures on all the saddle connections of length at most . Then as …
Convergence of Siegel-Veech constants
Benjamin Dozier
We show that for any weakly convergent sequence of ergodic -invariant probability measures on a stratum of unit-area translation surfaces, the corresponding Siege…