Marcus Rockel

About

I am a mathematician working in mathematical statistics. My research is on copulas and rank correlation coefficients, in particular on how Chatterjee’s rank correlation ξ relates to classical measures of concordance such as Spearman’s ρ, Kendall’s τ, Spearman’s footrule, Gini’s γ and Blomqvist’s β, including sharp inequalities and the ranges of values they can jointly attain.

My articles are accompanied by Lean 4 formalizations of their main results, and I maintain open-source software for computing with copulas. I received my doctorate (Dr. rer. nat.) from the University of Freiburg in 2025 and studied mathematics at the University of Bonn. Alongside research, I work as a freelance data engineer (Python, data pipelines, LLM-based tooling).

Research interests

• Copulas and dependence modeling
• Exact (attainable) regions and sharp inequalities between rank correlations and dependence measures
• Chatterjee's rank correlation and measures of functional dependence
• Stochastic orderings, positive dependence, optimal transport methods for copula extremal problems
• Formal verification of probabilistic and statistical results in Lean 4

Publications

Journal articles & proceedings

1. The exact region between Chatterjee's and Blest's rank correlations
   M. Rockel · International Journal of Approximate Reasoning, 109744, 2026
   Journal Lean
2. The exact region and an inequality between Chatterjee's and Spearman's rank correlations
   J. Ansari, M. Rockel · Journal of Multivariate Analysis 214, 105630, 2026
   Journal Lean
3. On the exact region between Chatterjee's rank correlation and Spearman's footrule
   M. Rockel · Journal of Computational and Applied Mathematics, 117466, 2026
   Journal Lean
4. Dependence properties of bivariate copula families
   J. Ansari, M. Rockel · Dependence Modeling 12(1), 20240002, 2024
   Journal Lean
5. An empirical study on new model-free multi-output variable selection methods
   J. Ansari, E. Lütkebohmert, M. Rockel · In: Combining, Modelling and Analyzing Imprecision, Randomness and Dependence (SMPS 2024), Advances in Intelligent Systems and Computing, pp. 9–17, Springer, 2024
   Journal

Preprints

1. Rank weighting and asymmetry in Blest's rank correlation: two exact regions
   M. Rockel · arXiv:2609.27634, 2026
   arXiv Lean
2. The exact region determined by Spearman's rho and Gini's gamma
   J. Ansari, M. Rockel, S. Steinmaßl · arXiv:2609.19890, 2026
   arXiv Lean
3. The exact Spearman rho–footrule region via optimal transport with applications to finite rankings, mixability, and Chatterjee's rank correlation
   J. Ansari, M. Rockel · arXiv:2608.20176, 2026
   arXiv Lean
4. The exact region determined by Kendall's tau, Spearman's footrule and Blomqvist's beta
   J. I. Orenday Lares, M. Rockel · arXiv:2607.12841, 2026
   arXiv Lean
5. The exact region between Chatterjee's ξ and Blomqvist's β
   J. I. Orenday Lares, M. Rockel · arXiv:2606.30033, 2026
   arXiv Lean
6. Kendall and Spearman bounds for Chatterjee's rank correlation under positive dependence
   M. Rockel · arXiv:2606.22074, 2026
   arXiv
7. Measures of association for approximating copulas
   M. Rockel · arXiv:2505.08045, 2025
   arXiv Lean

Theses

1. Chatterjee's rank correlation and classical concordance: copula perspectives, bounds, and computation
   Doctoral thesis (Dr. rer. nat.), University of Freiburg, 2025
   DOI
2. Dimensional improvements of functional inequalities for log-concave distributions
   Master's thesis, University of Bonn, 2018
   DOI PDF

Software & formalization

Teaching

University of Freiburg, Faculty of Economics and Behavioral Sciences

Education & positions

since 01/2026

Postdoctoral Researcher, Department of Quantitative Finance, University of Freiburg

2021 – 2025

Doctoral Researcher, University of Freiburg · Dr. rer. nat. (2025)

since 2022

Freelance Data Engineer

2016 – 2018

M.Sc. Mathematics, University of Bonn

2012 – 2016

B.Sc. Mathematics, University of Bonn