Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Delocalisation of eigenfunctions on large genus random surfaces   We prove that eigenfunctions of the Laplacian on a compact hyperbolic surface
delocalise in terms of a geometric parameter dependent upon the number of short
closed geodesics on the surface. In particular, we show that an $L^2$
normalised eigenfunction restricted to a measurable subset of the surface has
squared $L^2$-norm $\varepsilon>0$, only if the set has a relatively large size
-- exponential in the geometric parameter. For random surfaces with respect to
the Weil-Petersson probability measure, we then show, with high probability as
$g\to\infty$, that the size of the set must be at least the genus of the
surface to some power dependent upon the eigenvalue and $\varepsilon$.

12
The categories of this paper are: nucl-th
16
The categories of this paper are: stat
29
The categories of this paper are: funct-an
13
The categories of this paper are: quant-ph
10
The categories of this paper are: q-bio
31
The categories of this paper are: ao-sci
8
The categories of this paper are: hep-ex
26
The categories of this paper are: bayes-an
15
The categories of this paper are: nucl-ex
35
The categories of this paper are: mtrl-th
34
The categories of this paper are: chem-ph
0
The categories of this paper are: hep-ph
30
The categories of this paper are: q-alg
22
The categories of this paper are: chao-dyn
5
The categories of this paper are: gr-qc
36
The categories of this paper are: cmp-lg