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, including various kinds of trees, graphs, maps, partitions, and permutations. Here are some keywords that characterize my activities:
  • Limits of random structures (Gromov-Hausdorff-Prokhorov convergence, local topologies, permuton and graphon convergence, ...)
  • Branching processes and applications to random maps and graphs
  • Enumerative Combinatorics
  • Gibbs partition models
  • Phase transitions and condensation phenomena in weighted random graphs
  • Boltzmann sampling, combinatorial species, random isomorphism classes of structures
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).

Papers in journals / Preprints:
  1. Local convergence of random planar graphs
    [arXiv]
  2. Rerooting multi-type branching trees: the infinite spine case
    [arXiv]
  3. Graphon convergence of random cographs
    [arXiv]
  4. A decorated tree approach to random permutations in substitution-closed classes (joint with J. Borga, M. Bouvel, V. Féray)
    [arXiv]
  5. On the maximal offspring in a subcritical branching process
    [arXiv]
  6. Simply generated unrooted plane trees (joint with L. Ramzews)
    ALEA Latin American Journal of Probability and Mathematical Statistics, Volume XVI (2019), 333–359
    [link] [arXiv]
  7. Graph limits of random unlabelled k-trees (joint with E. Y. Jin)
    [arXiv]
  8. Pattern occurrences in random planar maps (joint with M. Drmota)
    To appear in Statistics and Probability Letters
    [arXiv]
  9. Asymptotic properties of random unlabelled block-weighted graphs
    [arXiv]
  10. Geometry of large Boltzmann outerplanar maps (joint with Sigurður Örn Stefánsson)
    Random Structures & Algorithms, Volume 55, Issue 3 (2019), 742–771
    [link] [arXiv]
  11. Limits of random tree-like discrete structures
    [hal] [arXiv]
  12. Unlabelled Gibbs partitions
    To appear in Combinatorics, Probability and Computing
    [hal] [arXiv]
  13. Local limits of large Galton-Watson trees rerooted at a random vertex
    Annales de l'Institut Henri Poincaré - Probabilités et Statistiques 2019, Vol. 55, No. 1, 155–183
    [link] [bibtex] [hal] [arXiv]
  14. Gibbs partitions: the convergent case
    Random Structures & Algorithms, Volume 53, Issue 3 (2018), 537–558
    [link] [bibtex] [hal] [arXiv]
  15. Graph limits of random graphs from a subset of of connected k-trees (joint with M. Drmota, E. Y. Jin)
    Random Structures & Algorithms 2019, Volume 55, 125–558
    [link] [bibtex] [hal] [arXiv]
  16. Random enriched trees with applications to random graphs
    Electronic Journal of Combinatorics, Volume 25, Issue 3 (2018), 81 pp.
    [link] [pdf] [bibtex] [arXiv]
  17. The continuum random tree is the scaling limit of unlabelled unrooted trees
    Random Structures & Algorithms, Volume 55, Issue 2 (2019), 496–528
    [link] [bibtex] [arXiv]
  18. Scaling limits of random Pólya trees (joint with K. Panagiotou)
    Probability Theory and Related Fields, 170 (2018), pp. 801–820
    [link] [bibtex] [arXiv]
  19. 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
    [link] [pdf] [bibtex] [arXiv]
  20. 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
    [link] [pdf] [bibtex] [arXiv]

Extended abstracts in conference proceedings:
  1. 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
  2. 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.

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]

Coauthors: