3 papers
math.PR2026
The tight length spectrum of large-genus random hyperbolic surfaces with many cusps
Timothy Budd, Tanguy Lions
Since the work of Mirzakhani and Petri on random hyperbolic surfaces of large genus, length statistics of closed geodesics have been studied extensively. We focus on the case of ra…
math.GT2025
A tree bijection for the moduli space of genus-0 hyperbolic surfaces with boundaries
Timothy Budd, Thomas Meeusen, Bart Zonneveld
The Weil-Petersson volume of genus-g hyperbolic surfaces with geodesic boundaries is known since work of Mirzakhani to be polynomial in the boundary lengths. We provide a bijective…
math.PR2025
Random punctured hyperbolic surfaces & the Brownian sphere
Timothy Budd, Nicolas Curien
We consider random genus-0 hyperbolic surfaces with punctures, sampled according to the Weil-Petersson measure. We show that, after rescaling the metric by…