Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Equidistribution of random waves on small balls   In this paper, we investigate the small scale equidistribution properties of
randomised sums of Laplacian eigenfunctions (i.e. random waves) on a compact
manifold. We prove small scale expectation and variance results for random
waves on all compact manifolds. Here, "small scale" refers to balls of radius
$r(\lambda)\to 0$ such that $r/r_{\text{Planck}}\to\infty$, where
$r_{\text{Planck}}$ is the Planck scale. For balls at a larger scale (although
still $r(\lambda)\to 0$) we also obtain estimates showing that the probability
that a random wave fails to equidistribute decays exponentially with the
eigenvalue.

33
The categories of this paper are: plasm-ph
15
The categories of this paper are: nucl-ex
12
The categories of this paper are: nucl-th
25
The categories of this paper are: patt-sol
0
The categories of this paper are: hep-ph
3
The categories of this paper are: physics
6
The categories of this paper are: astro-ph
26
The categories of this paper are: bayes-an
37
The categories of this paper are: supr-con
4
The categories of this paper are: cond-mat
20
The categories of this paper are: acc-phys
29
The categories of this paper are: funct-an
28
The categories of this paper are: alg-geom
27
The categories of this paper are: comp-gas
16
The categories of this paper are: stat
8
The categories of this paper are: hep-ex