arXiv
Open Access
2021
Spectral gap for Weil-Petersson random surfaces with cusps
Will Hide
Abstrak
We show that for any $ε>0$, $α\in[0,\frac{1}{2})$, as $g\to\infty$ a generic finite-area genus g hyperbolic surface with $n=O\left(g^α\right)$ cusps, sampled with probability arising from the Weil-Petersson metric on moduli space, has no non-zero eigenvalue of the Laplacian below $\frac{1}{4}-\left(\frac{2α+1}{4}\right)^{2}-ε$. For $α=0$ this gives a spectral gap of size $\frac{3}{16}-ε$ and for any $α<\frac{1}{2}$ gives a uniform spectral gap of explicit size.
Topik & Kata Kunci
Penulis (1)
W
Will Hide
Akses Cepat
Informasi Jurnal
- Tahun Terbit
- 2021
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- en
- Sumber Database
- arXiv
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- Open Access ✓