DeepAI AI Chat
Log In Sign Up

Ranks, copulas, and permutons

by   Rudolf Grübel, et al.

We review a recent development at the interface between discrete mathematics on one hand and probability theory and statistics on the other, specifically the use of Markov chains and their boundary theory in connection with the asymptotics of randomly growing permutations. Permutations connect total orders on a finite set, which leads to the use of a pattern frequencies. This view is closely related to classical concepts of nonparametric statistics. We give several applications and discuss related topics and research areas, in particular the treatment of other combinatorial families, the cycle view of permutations, and an approach via exchangeability.


page 1

page 2

page 3

page 4


Should Type Theory replace Set Theory as the Foundation of Mathematics

We discuss why Type Theory is preferable as foundation of Mathematics co...

Interactions of Computational Complexity Theory and Mathematics

[This paper is a (self contained) chapter in a new book, Mathematics an...

On the proper treatment of improper distributions

The axiomatic foundation of probability theory presented by Kolmogorov h...

Connecting Discrete Morse Theory and Persistence: Wrap Complexes and Lexicographic Optimal Cycles

We study the connection between discrete Morse theory and persistent hom...

Common Information, Noise Stability, and Their Extensions

Common information (CI) is ubiquitous in information theory and related ...

A synthetic approach to Markov kernels, conditional independence, and theorems on sufficient statistics

We develop Markov categories as a framework for synthetic probability an...

Strictly Frequentist Imprecise Probability

Strict frequentism defines probability as the limiting relative frequenc...