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Random surfaces with large systoles
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We present two constructions, both inspired by ideas from graph theory, of sequences random surfaces of growing area, whose systoles grow logarithmically as a function of their area. This also allows us to prove a new lower bound on the maximal systole of a closed orientable hyperbolic surface of a given genus.
Forward citations
Cited by 3 Pith papers
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A filling multi-geodesic on a genus g hyperbolic surface has length at least half the perimeter of a regular right-angled (8g-4)-gon, and this bound is sharp.
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Bass notes of random hyperbolic surfaces of large genus
A survey of recent results proving that random hyperbolic surfaces of large genus have near-optimal spectral gaps, after Hide–Magee, Anantharaman–Monk, and Hide–Macera–Thomas.
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