Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A version of Herbert A. Simon's model with slowly fading memory and its
  connections to branching processes   Construct recursively a long string of words w1. .. wn, such that at each
step k, w k+1 is a new word with a fixed probability p $\in$ (0, 1), and
repeats some preceding word with complementary probability 1 -- p. More
precisely, given a repetition occurs, w k+1 repeats the j-th word with
probability proportional to j $\alpha$ for j = 1,. .. , k. We show that the
proportion of distinct words occurring exactly times converges as the length n
of the string goes to infinity to some probability mass function in the
variable $\ge$ 1, whose tail decays as a power function when 1 -- p >
$\alpha$/(1 + $\alpha$), and exponentially fast when 1 -- p < $\alpha$/(1 +
$\alpha$).

31
The categories of this paper are: ao-sci
21
The categories of this paper are: adap-org
8
The categories of this paper are: hep-ex
28
The categories of this paper are: alg-geom
17
The categories of this paper are: q-fin
34
The categories of this paper are: chem-ph
25
The categories of this paper are: patt-sol
1
The categories of this paper are: cs
20
The categories of this paper are: acc-phys
12
The categories of this paper are: nucl-th
27
The categories of this paper are: comp-gas
30
The categories of this paper are: q-alg
22
The categories of this paper are: chao-dyn
33
The categories of this paper are: plasm-ph
4
The categories of this paper are: cond-mat
5
The categories of this paper are: gr-qc