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Below is an example that I had in mind, but my question is more general: does the reputation of some authors cause their papers to be prioritized for review sooner than other important papers, e.g. the paper "primes is in p" (link below), which was written by unknown, Indian grad students? In this specific example, a year seems like a long time to review an important -- and very short -- paper.

http://annals.math.princeton.edu/2004/160-2/p12

Milestones

Received: 24 January 2002

Accepted: 21 March 2003

Published online: September 2004

There can be many reasons why a paper takes a long time to be published. The `official' reason is that the paper needs to be carefully reviewed and considered before the result can be accepted for publication; the more prestigious the venue, the more care is taken in reviewing the results. However, there are other factors that come into play

1. This is in my view the most important: reviewers take a long time to get to finish their review, especially in high-quality venues. One should remember that reviewing is unpaid labour that academics provide to the academic publication industry for (what is apparently) the right to publish. There is no real incentive to review; there are meta considerations, like standing in the community, that depend on how much you do it, but I know several successful academics that do the bare minimum.


2. Good results in bad packaging: even a groundbreaking set of results can be poorly structured, which would result in delay in publication (if not outright rejection).


3. Politics and names do have some (minor) effect: having prominent authors/friends on the editorial board can result in a slightly faster turnaround. However, I have not heard of cases where editors have unethically accepted the work submitted by their friends, or rejected/dragged on the review process for the work of competitors.

You don't know what the timeline really was like. For all you know, it could've been this:

Authors submit paper: 24 January 2002

First decision made: 24 February 2002

Revision submitted: 3 March 2003

Final decision made: 21 March 2003

First proofs sent to author: 2 April 2003

Proofs received back from the author: August 2004

Don't automatically assume that long review times are always the journal's fault. Sometimes the author just takes a long time to respond. Here's an extreme example.

It's been more than three years since a decision was made on this manuscript, and the authors still haven't submitted a revision. At this point, they probably will never submit a revision. But if they do: the only fair submission date is 21 March 2015, and it will look like the review took a fantastically long time.

does the reputation of some authors cause their papers to be prioritized for review sooner than other important papers[?]

There isn't really such a thing as "prioritized for review". In most cases, the time it takes to find reviewers is much shorter than the time taken for those reviewers to do their work. Even if the editor says, "Wow, this paper is important – I'd better find reviewers as fast as I can!", that probably wouldn't make much difference to the total turn-around time.

e.g. the paper "primes is in p", which was written by unknown, Indian grad students

Maninindra Agrawal was a full professor at the time, not an unknown grad student.

The Annals of Mathematics is the most prestigious mathematical journal. It has very strict standards, and it often does triple reviews. So, the editor has to find three willing referees among top mathematicians in the area. These are usually very busy people, so it is no surprise that the whole process takes a while. Besides the fact that from "received" to "accepted" there may have been a request for a revision. In all, it doesn't sound like a lot of time, even if not ideal.

As an anecdote about this journal, I know about very good mathematicians who have submitted their best work to the Annals, and the report has been "good work, but not up to standards".

I doubt that the reputation of the author has a large effect in general, especially at the review stage. It might if the paper suggests an especially important result. In that case, a quick read and the likelihood that it is correct will motivate the editor and reviewers to get it finished quickly. But the sheer volume of submissions suggests that the effect is small, and rare.

More likely, delays are natural. If the topic is obscure it may be hard to find appropriate reviewers. If the result is a small contribution, there will be little incentive to advance it over others. Sometimes the paper requires additional checking, if it isn't especially self-contained or if the techniques used are non-standard.

Moreover, the editor doesn't have a lot of control over the work habits or schedules of the reviewers as they are usually unpaid volunteers. Academic schedules get in the way of doing things quickly as does the too common absent mindedness of some professors. Sometimes the reviews come back to the editor in a way that it is hard to make a decision and the paper is sent out to others so that the editor gets a clearer picture. Sometimes reviewer conflicts need to be addressed internally.

Once accepted, the delays are usually just caused by scheduling. For print journals, especially, where overall page limits put in a constraint, as well as the fact that some editors may want to bring similarly themed papers into a single volume. At this point, of course, it may be desirable to think about the reputation of the authors and so an unknown author with a minor result might get delayed a bit.