Prof. Dr. Sebastian Mentemeier

Research interests

• Non-Gaussian limit theorems
• Branching processes, in particular Multitype Branching Random Walks
• Products of random matrices
• Extreme value theory, in particular for time series
• Heavy-tailed random variables
• Conditional limit theorems

Third-party funds

• DFG-Project: "Nichtlineare stochastische Fixpunktgleichungen mit Anwendungen in der Statistischen Mechanik" (2017-2023)
• DFG-Project: "Produkte von Zufallsmatrizen, nichtkommutative Verzweigende Irrfahrten und Multityp-Verzweigende Irrfahrten in zufälligen Umgebungen" (seit 2021)

1. The extremal position of a branching random walk in the general linear group
   joint work with Ion Grama and Hui Xiao
   arxiv
2. Limit theorems for first passage times of multivariate perpetuity sequences
   joint work with Hui Xiao
   arxiv
3. Analysing heavy-tail properties of Stochastic Gradient Descent by means of Stochastic Recurrence Equations
   joint work with Ewa Damek
   arxiv

1. Asymptotic independence ex machina: Extreme value theory for the diagonal SRE model
   joint work with Olivier Wintenberger
   Journal of Time Series Analysis 43(5), 750-780 (2022). arxiv wiley
2. Absolute Continuity of Complex Martingales and of Solutions to Complex Smoothing Equations
   joint work with Ewa Damek
   Electronic Communications in Probability 23(60), 1-12 (2018). arxiv ecp
3. Large excursions and conditioned laws for recursive sequences generated by random matrices
   joint work with Jeffrey Collamore
   Ann. Probab. 46, 2064-2120 (2018)  arxiv
4. Precise Tail Asymptotics for Attracting Fixed Points of Multivariate Smoothing Transformations
   joint work with Dariusz Buraczewski
   Markov Processes Relat. Fields 23, 147-170 (2017) arxiv
5. Solutions to Complex Smoothing Equations
   joint work with Matthias Meiners
   Probab. Theory Relat. Fields, 168(1-2), 199-268 (2017) springerlink arxiv
6. Fixed Points of the Multivariate Smoothing Transform: The Critical Case
   joint work with Konrad Kolesko
   Electronic Journal of Probability 20(52), 1-24 (2015) arxiv ejpecp
7. Precise Large Deviation Results for Products of Random Matrices
   joint work with Dariusz Buraczewski
   Annales de l'Institut Henri Poincare Probab. Statist. 52(3), 1474-1513 (2016). arxiv projecteuclid
8. Fixed Points of the Multivariate Smoothing Transform
   Probab. Theory Rel. Fields 164(1), 401-458 (2016) arxiv springerlink
9. On Multidimensional Mandelbrot Cascades
   joint work with Dariusz Buraczewski, Ewa Damek and Yves Guivarc'h
   J. Diff. Equation Appl. 20(11), 1523-1567 (2014) arxiv tandfonline
10. On Kesten's Multivariate Choquet-Deny Lemma
    Electronic Communications in Probability 18(65), 1-7 (2013) arxiv ejpecp
11. Heavy tailed solutions of multivariate smoothing transforms
    joint work with Dariusz Buraczewski, Ewa Damek and Mariusz Mirek
    Stochastic Processes and their Applications 123(6), 1947-1986 (2013) arxiv sciencedirect
12. Precise tail index of fixed points of the two-sided smoothing transform
    joint work with Gerold Alsmeyer and Ewa Damek
    Random Matrices and Iterated Random Functions. Springer Proceedings in Mathematics & Statistics, Vol. 53 arxiv springerlink
13. Convergence to stable laws for multidimensional stochastic recursions: the case of regular matrices
    joint work with Ewa Damek, Mariusz Mirek and Jacek Zienkiewicz
    Potential Analysis 38(3), 683-697 (2013) arxiv springerlink
14. Tail behavior of stationary solutions of random difference equations: the case of regular matrices
    joint work with Gerold Alsmeyer
    J. Diff. Equation Appl. 18(8), 1305-1332 (2012) arxiv tandfonline

• On Multivariate Stochastic Fixed Point Equations: The Smoothing Transform and Random Difference Equations
  PhD thesis, December 2012. pdf
• Erneuerungstheorie für Produkte von Zufallsmatrizen (German)
  Diploma thesis, September 2009. pdf

Reviewer / Referee for: Colloquium Mathematicum, Extremes, J. Theor. Prob., J. Diff. Equation Appl., Markov Proc. Rel. Fields, MathSciNet, Springer Books, Stoch. Proc. Appl., Zentralblatt Math

Conferences I am / have been (co-)organizing