Research

UMPA

Research interests:
My research interests lie at the interface of combinatorics and probability theory. I combine stochastic process methods with combinatorial constructions to study models of random discrete structures such as graphs, maps, partitions, and permutations.

My focus lies on asymptotic geometric properties such as scaling limits and local weak limits. Motivation for this line of research comes from problems in computer science (average case analysis of algorithms) and physics (two-dimensional quantum gravity).

I enjoy writing open source software (github project page) that simulates random discrete structures. I have taught courses on interesting topics like Hopf algebras (with lecture notes).

Publications / Preprints:
  1. Scaling limits of random graphs from subcritical classes (joint with K. Panagiotou, K. Weller)
    The Annals of Probability 2016, Vol. 44, No. 5, 3291–3334
    [pdf] [bibtex] [arXiv]
  2. Scaling limits of random outerplanar maps with independent link weights
    Annales de l'Institut Henri Poincaré - Probabilités et Statistiques 2017, Vol. 53, No. 2, 900–915
    [pdf] [bibtex] [arXiv]
  3. Scaling limits of random Pólya trees (joint with K. Panagiotou)
    Probability Theory and Related Fields, 170 (2018), pp. 801–820
    [link] [bibtex] [arXiv]
  4. The continuum random tree is the scaling limit of unlabelled unrooted trees
    To appear in Random Structures & Algorithms
    [arXiv]
  5. Random enriched trees with applications to random graphs
    Electronic Journal of Combinatorics, Volume 25, Issue 3 (2018), 81 pp.
    [pdf] [link] [bibtex] [arXiv]
  6. Graph limits of random graphs from a subset of of connected k-trees (joint with M. Drmota, E. Y. Jin)
    To appear in Random Structures & Algorithms
    [hal] [arXiv]
  7. Gibbs partitions: the convergent case
    Random Structures & Algorithms, Volume 53, Issue 3 (2018), 537–558
    [link] [bibtex] [hal] [arXiv]
  8. Unlabelled Gibbs partitions
    To appear in Combinatorics, Probability and Computing
    [hal] [arXiv]
  9. Local limits of large Galton-Watson trees rerooted at a random vertex
    To appear in Annales de l'Institut Henri Poincaré - Probabilités et Statistiques
    [hal] [arXiv]
  10. Limits of random tree-like discrete structures
    [hal] [arXiv]
  11. Geometry of large Boltzmann outerplanar maps (joint with Sigurður Örn Stefánsson)
    To appear in Random Structures & Algorithms
    [arXiv]
  12. Asymptotic properties of random unlabelled block-weighted graphs
    [arXiv]
  13. Benjamini-Schramm convergence of random planar maps (joint with M. Drmota)
    [arXiv]
  14. Graph limits of random unlabelled k-trees (joint with E. Y. Jin)
    [arXiv]
  15. Simply generated unrooted plane trees (joint with L. Ramzews)
    [arXiv]

Extended abstracts in conference proceedings:
  1. Scaling limits of random graphs from subcritical classes: Extended abstract (joint with K. Panagiotou, K. Weller)
    27th International Conference on Formal Power Series and Algebraic Combinatorics, DMTCS proc. FPSAC '15, p. 745–756, 2015.
  2. Local limits of large Galton-Watson trees rerooted at a random vertex: Extended abstract
    29th International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA 2018), vol. 110 of Leibniz International Proceedings in Informatics (LIPIcs), p. 34:1–34:11

Theses:
  1. Scaling limits of random trees and graphs
    PhD thesis, Ludwig Maximilian University of Munich, 2015
    [link]
  2. Coxeter groupoids
    Diploma thesis ("Diplomarbeit"), Ludwig Maximilian University of Munich, 2013
    [pdf]

My coauthors: