  Recently we proposed a model in which when a scientist writes a manuscript,
he picks up several random papers, cites them and also copies a fraction of
their references (cond-mat/0305150). The model was stimulated by our discovery
that a majority of scientific citations are copied from the lists of references
used in other papers (cond-mat/0212043). It accounted quantitatively for
several properties of empirically observed distribution of citations. However,
important features, such as power-law distribution of citations to papers
published during the same year and the fact that the average rate of citing
decreases with aging of a paper, were not accounted for by that model. Here we
propose a modified model: when a scientist writes a manuscript, he picks up
several random recent papers, cites them and also copies some of their
references. The difference with the original model is the word recent. We solve
the model using methods of the theory of branching processes, and find that it
can explain the aforementioned features of citation distribution, which our
original model couldn't account for. The model can also explain "sleeping
beauties in science", i.e., papers that are little cited for a decade or so,
and later "awake" and get a lot of citations. Although much can be understood
from purely random models, we find that to obtain a good quantitative agreement
with empirical citation data one must introduce Darwinian fitness parameter for
the papers.
