Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Greedy algorithms and Zipf laws   We consider a simple model of firm/city/etc. growth based on a multi-item
criterion: whenever entity B fares better that entity A on a subset of $M$
items out of $K$, the agent originally in A moves to B. We solve the model
analytically in the cases $K=1$ and $K \to \infty$. The resulting stationary
distribution of sizes is generically a Zipf-law provided $M > K/2$. When $M
\leq K/2$, no selection occurs and the size distribution remains thin-tailed.
In the special case $M=K$, one needs to regularise the problem by introducing a
small "default" probability $\phi$. We find that the stationary distribution
has a power-law tail that becomes a Zipf-law when $\phi \to 0$. The approach to
the stationary state can also been characterized, with strong similarities with
a simple "aging" model considered by Barrat & M\'ezard.

22
The categories of this paper are: chao-dyn
10
The categories of this paper are: q-bio
12
The categories of this paper are: nucl-th
13
The categories of this paper are: quant-ph
3
The categories of this paper are: physics
16
The categories of this paper are: stat
2
The categories of this paper are: math
33
The categories of this paper are: plasm-ph
5
The categories of this paper are: gr-qc
37
The categories of this paper are: supr-con
15
The categories of this paper are: nucl-ex
25
The categories of this paper are: patt-sol
30
The categories of this paper are: q-alg
18
The categories of this paper are: econ
19
The categories of this paper are: eess
27
The categories of this paper are: comp-gas