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pro vyhledávání: '"Hide, Will"'
Autor:
Hide, Will, Thomas, Joe
We study topological lower bounds on the number of small Laplacian eigenvalues on hyperbolic surfaces. We show there exist constants $a,b>0$ such that when $(g+1)
Externí odkaz:
http://arxiv.org/abs/2410.06093
Autor:
Hide, Will, Thomas, Joe
We study the geometry and spectral theory of Weil-Petersson random surfaces with genus-$g$ and $n$ cusps in the large-$n$ limit. We show that for a random hyperbolic surface in $\mathcal{M}_{g,n}$ with $n$ large, the number of small Laplacian eigenva
Externí odkaz:
http://arxiv.org/abs/2312.11412
Autor:
Hide, Will
Let $X$ be a finite-area non-compact hyperbolic surface. We study the spectrum of the Laplacian on random covering surfaces of X and on random unitary bundles over X. We show that there is a constant $c > 0$ such that, with probability tending to 1 a
Externí odkaz:
http://arxiv.org/abs/2305.04584
Autor:
Hide, Will, Thomas, Joe
We study the number of short geodesics and small eigenvalues on Weil-Petersson random genus zero hyperbolic surfaces with $n$ cusps in the regime $n\to\infty$. Inspired by work of Mirzakhani and Petri \cite{Mi.Pe19}, we show that the random multi-set
Externí odkaz:
http://arxiv.org/abs/2209.15568
Autor:
Hide, Will
We show that for any $\epsilon>0$, $\alpha\in[0,\frac{1}{2})$, as $g\to\infty$ a generic finite-area genus g hyperbolic surface with $n=O\left(g^{\alpha}\right)$ cusps, sampled with probability arising from the Weil-Petersson metric on moduli space,
Externí odkaz:
http://arxiv.org/abs/2107.14555
Autor:
Hide, Will, Magee, Michael
We prove that if $X$ is a finite area non-compact hyperbolic surface, then for any $\epsilon>0$, with probability tending to one as $n\to\infty$, a uniformly random degree $n$ Riemannian cover of $X$ has no eigenvalues of the Laplacian in $[0,\frac{1
Externí odkaz:
http://arxiv.org/abs/2107.05292
Autor:
Hide, Will
Publikováno v:
IMRN: International Mathematics Research Notices; Oct2023, Vol. 2023 Issue 20, p17411-17460, 50p
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