The rescaled distance between random points in high-genus triangulations converges in probability to a deterministic constant.
Counting curves, and the stable length of currents
5 Pith papers cite this work, alongside 1 external citations. Polarity classification is still indexing.
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UNVERDICTED 5representative citing papers
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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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.