Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Uniform Random Pointwise Ergodic Theorem   Let $a_n$ be the random increasing sequence of natural numbers which takes
each value independently with decreasing probability of order $n^{-\alpha}$, $0
< \alpha < 1/2$. We prove that, almost surely, for every measure-preserving
system $(X,T)$ and every $f \in L^1(X)$ orthogonal to the invariant factor, the
modulated, random averages \[ \sup_{b} \Big| \frac{1}{N} \sum_{n = 1}^N b(n)
T^{a_{n}} f \Big| \] converge to $0$ pointwise almost everywhere, where the
supremum is taken over a set of bounded functions with certain uniform
approximation properties.

1
The categories of this paper are: cs
29
The categories of this paper are: funct-an
17
The categories of this paper are: q-fin
23
The categories of this paper are: solv-int
4
The categories of this paper are: cond-mat
13
The categories of this paper are: quant-ph
0
The categories of this paper are: hep-ph
28
The categories of this paper are: alg-geom
30
The categories of this paper are: q-alg
31
The categories of this paper are: ao-sci
20
The categories of this paper are: acc-phys
35
The categories of this paper are: mtrl-th
24
The categories of this paper are: dg-ga
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