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Activity Number: 20
Type: Topic Contributed
Date/Time: Sunday, July 31, 2016 : 2:00 PM to 3:50 PM
Sponsor: Section on Statistical Learning and Data Science
Abstract #320004 View Presentation
Title: The Large N Limit of the Mallows Model
Author(s): Shannon Starr* and Meg L. Walters
Companies: University of Alabama at Birmingham and University of Rochester
Keywords: Mallows model ; non-parametric statistics ; Frank copula ; permuton ; basic hypergeometric functions

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.

Authors who are presenting talks have a * after their name.

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