The rescaled distance between random points in high-genus triangulations converges in probability to a deterministic constant.
Friedman-Ramanujan functions in random hyper- bolic geometry and application to spectral gaps II
6 Pith papers cite this work. Polarity classification is still indexing.
6
Pith papers citing it
years
2026 6verdicts
UNVERDICTED 6representative citing papers
An explicit frequency expression for non-simple curves is derived, with large-genus asymptotics showing which fixed-K intersection types are most common.
The sets of eigenvalues of weighted graph Laplacians are fully described for every valid four-vertex graph coming from a pair-of-pants decomposition of a genus-3 surface.
Generalizes integration formulas for geometric random variables on moduli space of hyperbolic surfaces to arbitrary closed loops and improves asymptotic for Weil-Petersson expectation of geodesic counts in an orbit.
Eigenfunctions of Schrödinger operators on BS-converging hyperbolic surfaces exhibit quantum mixing in sufficiently large spectral windows.
Typical hyperbolic surfaces under the Weil-Petersson measure have spectral gap at least 2/9 - ε.
citing papers explorer
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Typical distances in high-genus triangulations
The rescaled distance between random points in high-genus triangulations converges in probability to a deterministic constant.
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Large genus asymptotics for frequency of non-simple curves
An explicit frequency expression for non-simple curves is derived, with large-genus asymptotics showing which fixed-K intersection types are most common.
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Flexibility of eigenvalues for graph Laplacians arising from genus 3 surfaces
The sets of eigenvalues of weighted graph Laplacians are fully described for every valid four-vertex graph coming from a pair-of-pants decomposition of a genus-3 surface.
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Integrals of general geometric random variables on the moduli space of hyperbolic surfaces
Generalizes integration formulas for geometric random variables on moduli space of hyperbolic surfaces to arbitrary closed loops and improves asymptotic for Weil-Petersson expectation of geodesic counts in an orbit.
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Quantum Mixing for Schr\"odinger eigenfunctions in Benjamini-Schramm limit
Eigenfunctions of Schrödinger operators on BS-converging hyperbolic surfaces exhibit quantum mixing in sufficiently large spectral windows.
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Typical hyperbolic surfaces have a spectral gap greater than $2/9 - \epsilon$
Typical hyperbolic surfaces under the Weil-Petersson measure have spectral gap at least 2/9 - ε.