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Abstract:
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The Mallows model is an important model in non-parametric hypothesis testing. For a special case, the Mallows model relative to Kendall's tau, there are algebraic formulas for the theoretical probabilities. If one chooses the parameter of the model to scale with the system size as q=1-C/n then other authors have shown a dense graph limit. In particular Mukherjee and Battacharya have found an intricate structure including a phase transition. Bamattre, Hu and Verducci have identified the limit as the Frank copula. It is also possible to do some large deviation calculations for this model, which give another perspective on the Frank copula and are also related to basic hypergeometric functions as studied by Gasper and Rahman and many others. We will review some history of this model.
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