18 citations · 42 across the 12 of their papers we have counts for
15 papers
Large-scale rank and geometry of the Lipschitz metric on geodesic currents
Dídac Martínez-Granado, Jenya Sapir
For a closed orientable surface of genus at least 2, we study the large-scale geometry of the (symmetrized) Lipschitz metric on its space of projective filling geodesic currents. W…
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…
An extension of the Thurston metric to projective filling currents
Jenya Sapir
We study the geometry of the space of projectivized filling geodesic currents . Bonahon showed that Teichmüller space, embeds into $…
A length comparison theorem for geodesic currents
Jenya Sapir
We work with the space of geodesic currents on a closed surface of negative Euler characteristic. By prior work of the author with Sebastian Hensel, each fillin…
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 …
A projection from filling currents to Teichmüller space
Sebastian Hensel, Jenya Sapir
Let be a closed, genus surface. The space of geodesic currents on encompasses the set of closed curves up to homotopy, as well as Teichmüller space, and many other spac…