Category Archives: About the Profession

The Viagra Standard: Redux

It seems fitting to open my new blog by going back to one of the first columns I wrote for the IMS Bulletin. At least I think that it was one of my firsts, the online archive doesn’t go back before 2010 and having changed computers since then, I can’t find the file.

The issue then as it is today is: What is good probability? Several of my recent papers have been rejected by referees who said: “this is interesting, but it isn’t hard.” Years ago I coined the phrase the Viagra standard for this – if it is not hard it is not good. The phrase never got into print because the editor thought it was a little risqué. I agree that there is something obscene here, but it is the policy not the phrase. Do we really want journals filled with papers that are hard but not interesting? Evidently we do, because that’s what we have got!

Rather than argue abstractly, let me talk about one concrete example. During the 2010-2011 academic year, David Sivakoff and I had almost weekly meetings with a group of students from the North Carolina School of Science and Math. We eventually wrote a paper with two of the students from the group, Sam Magura and Vichtyr Pong. The paper was inspired one published in the Proceedings of the National Academy of Science by Henry, Pralat and Zhang [108: 8605-8610].

People have opinions in the d-dimensional unit cube. Connections are broken at a rate proportional to their length and rewired randomly, or reconnected by a Metropolis-Hastings dynamic that always accepts shorter connection and accepts longer one with a probability equal to the ratio of the lengths. The key to our analysis was that the system had a reversible stationary distribution that is closely related to long range percolation, modulo the difference that the evolving graph has a fixed number of edges while the percolation has a random number.

There was also a second model invented by the students, which involved individuals who preferred to be connected to people who are popular. Again there was a reversible stationary distribution, which this time was related a graph generated by a particular instance of the configuration model. The paper proved some results about the two systems and did simulations to treat what we could not.

In December 2012 we submitted the paper to Electronic Journal of Probability. The referee took seven months and decided: “My main concern is that too much of it is non-rigorous or is not sufficiently clearly stated to be rigorous. That said, the models discussed are interesting and there is some potential here.” We fixed the problems by using coupling to tighten up the connection between the evolving graphs with a fixed number of edges and the associated models that did not. We resubmitted the paper and heard nothing for five months. We wrote to the editor and we soon had a short report “Most of the comments I made in my review of a previous version of this paper have been addressed.” But the final decision was “The models are interesting as well as some of the results but the paper is perhaps not quite deep enough to merit publication in in EJP.”

Having lost more than a year at EJP, we turned to Journal of Applied Probability. Four months later we got a report from an expert in random graphs, who cited two of his own papers, and told us “I was disappointed reading the paper, since the authors proposed three interesting models but the analysis never went beyond what was easy to get and was already known.” It is frustrating to get absolutely no credit for making the connection and solving the problem. Yes we did use results about long range percolation, and Bollobas-Janson-Riordan, but these are hardly things everyone knows.

Perhaps the most depressing thing is that I looked at the list of papers to appear in JAP. Is our work really worse than what they print. The bottom line, boys and girls, is that if you want to get your work published, you should work in area that only ten people care about, and be friendly to them.