Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The limit distribution of the maximum probability nearest neighbor ball   Let $X_1, \ldots, X_n$ be independent random points drawn from an absolutely
continuous probability measure with density $f$ in $\mathbb{R}^d$. Under mild
conditions on $f$, we derive a Poisson limit theorem for the number of large
probability nearest neighbor balls. Denoting by $P_n$ the maximum probability
measure of nearest neighbor balls, this limit theorem implies a Gumbel extreme
value distribution for $nP_n - \ln n$ as $n \to \infty$. Moreover, we derive a
tight upper bound on the upper tail of the distribution of $nP_n - \ln n$,
which does not depend on $f$.

33
The categories of this paper are: plasm-ph
8
The categories of this paper are: hep-ex
17
The categories of this paper are: q-fin
0
The categories of this paper are: hep-ph
5
The categories of this paper are: gr-qc
7
The categories of this paper are: hep-th
18
The categories of this paper are: econ
19
The categories of this paper are: eess
36
The categories of this paper are: cmp-lg
28
The categories of this paper are: alg-geom
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The categories of this paper are: comp-gas
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The categories of this paper are: funct-an
1
The categories of this paper are: cs
35
The categories of this paper are: mtrl-th
26
The categories of this paper are: bayes-an
24
The categories of this paper are: dg-ga