5 years of Macdonald Processes

2016/11/18


Today marks a 5-year anniversary of the paper “Macdonald Processes” by A. Borodin and I. Corwin. It was posted on the arXiv on November 18, 2011 (arxiv.org/abs/1111.4408) and was subsequently published at Probability Theory and Related Fields (2014), Volume 158, Issue 1, pp 225–400. As of this day, Google Scholar counts 178 citations to this paper.

In this paper, the authors introduced Macdonald measures on partitions (and Macdonald processes on sequences of partitions) - an extremely rich family of distributions with connections to Kardar-Parisi-Zhang equation, random matrix theory (including general beta random matrices), random polymers, classical combinatorial construction, and more. The breakthrough achievement of this paper is that properties of Macdonald symmetric polynomials (building blocks of the Macdonald measures and processes) allow to write down concise exact formulas for expectations of various observables with respect to the Macdonald measures and processes. This provides tools for asymptotic analysis of Macdonald measures and processes and their various degenerations, and has led to many very interesting results in Integrable Probability during the past five years.

Congratulations, Alexei and Ivan!

PS Coincidentally, in August 2011, about 5 years ago, I moved from Moscow to Boston to be a postdoc at Northeastern University, which allowed me to witness (and soon enough participate in) exciting new developments around Macdonald processes and Integrable Probability.

A flowchart for Macdonald processes and some of their specializations and limits (from talks of the authors on the subject)
A flowchart for Macdonald processes and some of their specializations and limits (from talks of the authors on the subject)