Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Inner radius of nodal domains of quantum ergodic eigenfunctions   In this short note we show that the lower bounds of Mangoubi on the inner
radius of nodal domains can be improved for quantum ergodic sequences of
eigenfunctions, according to a certain power of the radius of shrinking balls
on which the eigenfunctions equidistribute. We prove such improvements using a
quick application of our recent results (arXiv:1606.02057), which give modified
growth estimates for eigenfunctions that equidistribute on small balls. Since
by the results of Han and Hezari-Rivi\`ere small scale QE holds for negatively
curved manifolds on logarithmically shrinking balls, we get logarithmic
improvements on the inner radius of such manifolds. We also get improvements
for manifolds with ergodic geodesic flows. In addition using the small scale
equidistribution results of Lester-Rudnick, one gets polynomial betterments of
for toral eigenfunctions in dimensions $n \geq 3$. The results work only for a
full density subsequence of eigenfunctions.

26
The categories of this paper are: bayes-an
10
The categories of this paper are: q-bio
16
The categories of this paper are: stat
17
The categories of this paper are: q-fin
8
The categories of this paper are: hep-ex
3
The categories of this paper are: physics
24
The categories of this paper are: dg-ga
4
The categories of this paper are: cond-mat
12
The categories of this paper are: nucl-th
29
The categories of this paper are: funct-an
37
The categories of this paper are: supr-con
28
The categories of this paper are: alg-geom
15
The categories of this paper are: nucl-ex
11
The categories of this paper are: hep-lat
20
The categories of this paper are: acc-phys
32
The categories of this paper are: atom-ph