Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the generalized circle problem for a random lattice in large
  dimension   In this note we study the error term R_{n,L}(x) in the generalized circle
problem for a ball of volume x and a random lattice L of large dimension n. Our
main result is the following functional central limit theorem: Fix an arbitrary
function f(n) from the positive integers to the positive real line, tending to
infinity with n but with subexponential growth. Then, the random function t ->
(2f(n))^{-1/2} R_{n,L}(t f(n)) on the interval [0,1] converges in distribution
to one-dimensional Brownian motion as n tends to infinity. The proof goes via
convergence of moments, and for the computations we develop a new version of
Rogers' mean value formula. For the individual k:th moment of the variable
(2f(n))^{-1/2} R_{n,L}(f(n)) we prove convergence to the corresponding Gaussian
moment more generally for functions f satisfying f(n)<<e^{cn} for any fixed c
in an interval 0<c<c_k, where c_k is a constant depending on k whose optimal
value we determine.

17
The categories of this paper are: q-fin
36
The categories of this paper are: cmp-lg
16
The categories of this paper are: stat
20
The categories of this paper are: acc-phys
18
The categories of this paper are: econ
28
The categories of this paper are: alg-geom
37
The categories of this paper are: supr-con
19
The categories of this paper are: eess
33
The categories of this paper are: plasm-ph
4
The categories of this paper are: cond-mat
3
The categories of this paper are: physics
35
The categories of this paper are: mtrl-th
12
The categories of this paper are: nucl-th
27
The categories of this paper are: comp-gas
5
The categories of this paper are: gr-qc
34
The categories of this paper are: chem-ph