Research

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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 structures, including various kinds of trees, graphs, maps, partitions, and permutations. An example of such structures is the randomly generated surface in the display. 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 their application 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

Research projects:

• 2024 – 2027: Principal Investigator of FWF Project Limits of random networks. Funding: 435,021 EUR
• 2024 – 2028: Principal Investigator of FWF Project Part Asymptotic enumeration and study of discrete structures of the SFB Discrete random structures: enumeration and scaling limits. Funding Project Part: 317,706 EUR. Total SFB Funding: 3,921,934 EUR.
• 2024 – 2027: Member of FWF-ANR Project Analysis of Certain Classes of DAGs. Funding of Austrian side: 379,239 EUR. Funding of French side: 295,534 EUR.
• 2023 – 2024: Member of OeAD WTZ/PHC Amadeus Project Asymptotic behaviour of combinatorial structures. Funding 8,000 EUR
• 2016 – 2017: Principal Investigator of DFG Research Fellowship Scaling limits and local weak limits of random structures. Funding: 82,229 EUR

Journal publications and preprints:

1. J. Castellvi and B. Stufler. Limits of chordal graphs with bounded tree-width
   
   Submitted
   [arXiv]
2. B. Stufler. Poisson-Dirichlet scaling limits of Kemp's supertrees
   
   Submitted
   [arXiv]
3. B. Stufler. Probabilistic enumeration and equivalence of nonisomorphic trees
   
   Submitted
   [arXiv]
4. D. Sénizergues, S. Ö. Stefänsson and B. Stufler. Decorated stable trees
   
   Electronic Journal of Probability (2023), Vol. 28, 1–53
   [link] [arXiv]
5. B. Stufler. Gibbs partitions: a comprehensive phase diagram
   
   Annales de l'Institut Henri Poincaré - Probabilités et Statistiques (2024), Vol. 60, No. 3, 1729–1766
   [link] [arXiv]
6. B. Stufler. The scaling limit of random cubic planar graphs
   
   To appear in Journal of the London Mathematical Society
   [arXiv]
7. B. Stufler. First-passage percolation on random simple triangulations
   
   ALEA Latin American Journal of Probability and Mathematical Statistics (2024), Vol. XXI, 129–178
   [link] [arXiv]
8. B. Stufler. The Uniform Infinite Cubic Planar Graph
   
   Bernoulli (2023), Vol. 29, No. 4, 2902–2926
   [link] [arXiv]
9. B. Stufler. Mass and radius of balls in Gromov-Hausdorff-Prokhorov convergent sequences
   
   Submitted
   [arXiv]
10. K. Panagiotou, L. Ramzews and B. Stufler. Exact-size sampling of enriched trees in linear time
    
    SIAM Journal on Computing (2023), Vol. 52, No. 5
    [link] [arXiv]
11. M. Drmota, M. Noy and B. Stufler. Cut vertices in random planar maps
    
    Electronic Journal of Combinatorics (2023), Vol. 30, No. 3
    [link] [arXiv]
12. B. Stufler. A branching process approach to level-k phylogenetic networks
    
    Random Structures & Algorithms (2022), Vol. 61, No. 2, 397–421
    [link] [arXiv]
13. B. Stufler. Local convergence of random planar graphs
    
    Journal of the European Mathematical Society (2023), Vol. 25, No. 1, 1–73
    [link] [arXiv]
14. B. Stufler. Quenched local convergence of Boltzmann planar maps
    
    Journal of Theoretical Probability (2022), Vol. 35, 1324–1342
    [link] [arXiv]
15. B. Stufler. Rerooting multi-type branching trees: the infinite spine case
    
    Journal of Theoretical Probability (2022), Vol. 35, 653–684
    [link] [arXiv]
16. B. Stufler. Graphon convergence of random cographs
    
    Random Structures & Algorithms (2021), Vol. 59, No. 3, 464–491
    [link] [arXiv]
17. J. Borga, M. Bouvel, V. Féray and B. Stufler. A decorated tree approach to random permutations in substitution-closed classes
    
    Electronic Journal of Probability (2020), Vol. 25, paper no. 67, 1–52.
    [link] [arXiv]
18. B. Stufler. On the maximal offspring in a subcritical branching process
    
    Electronic Journal of Probability (2020), Vol. 25, paper no. 104, 1–62.
    [link] [arXiv]
19. L. Ramzews and B. Stufler. Simply generated unrooted plane trees
    
    ALEA Latin American Journal of Probability and Mathematical Statistics (2019), Vol. XVI, 333–359
    [link] [arXiv]
20. E. Y. Jin and B. Stufler. Graph limits of random unlabelled k-trees
    
    Combinatorics, Probability and Computing (2020), Vol. 29, No. 5, 722–746
    [link] [arXiv]
21. M. Drmota and B. Stufler. Pattern occurrences in random planar maps
    
    Statistics and Probability Letters (2020), Vol. 158
    [link] [arXiv]
22. B. Stufler. Asymptotic properties of random unlabelled block-weighted graphs
    
    Electronic Journal of Combinatorics (2021), Vol. 28, No. 4
    [link] [arXiv]
23. S. Ö. Stefánsson and B. Stufler. Geometry of large Boltzmann outerplanar maps
    
    Random Structures & Algorithms (2019), Vol. 55, No. 3, 742–771
    [link] [arXiv]
24. B. Stufler. Limits of random tree-like discrete structures
    
    Probability Surveys (2020), Vol. 17, No. 0, 318–477
    [link] [arXiv]
25. B. Stufler. Unlabelled Gibbs partitions
    
    Combinatorics, Probability and Computing (2020), Vol. 29, No. 2, 293–309
    [link] [arXiv]
26. B. Stufler. 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] [arXiv]
27. B. Stufler. Gibbs partitions: the convergent case
    
    Random Structures & Algorithms (2018), Vol. 53, No. 3, 537–558
    [link] [arXiv]
28. M. Drmota, E. Y. Jin and B. Stufler. Graph limits of random graphs from a subset of of connected k-trees
    
    Random Structures & Algorithms (2019), Vol. 55, No. 1, 125–152
    [link] [arXiv]
29. B. Stufler. Random enriched trees with applications to random graphs
    
    Electronic Journal of Combinatorics (2018), Vol. 25, No. 3, 81 pp.
    [link] [arXiv]
30. B. Stufler. The continuum random tree is the scaling limit of unlabelled unrooted trees
    
    Random Structures & Algorithms (2019), Vol. 55, No. 2, 496–528
    [link] [arXiv]
31. K. Panagiotou and B. Stufler. Scaling limits of random Pólya trees
    
    Probability Theory and Related Fields (2018), Vol. 170, No. 3-4, pp. 801–820
    [link] [arXiv]
32. B. Stufler. 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] [arXiv]
33. K. Panagiotou, B. Stufler and K. Weller. Scaling limits of random graphs from subcritical classes
    
    The Annals of Probability (2016), Vol. 44, No. 5, 3291–3334
    [link] [arXiv]

Conference proceedings and reports:

1. B. Stufler. Local convergence of random planar graphs
   
   Proceedings of the European Conference on Combinatorics, Graph Theory and Applications (EuroComb 2021), vol. 14 of Trends in Mathematics, Birkhäuser, Cham, p. 57–63
2. M. Drmota, M. Noy and B. Stufler. Cut Vertices in Random Planar Maps
   
   31st International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA 2020), vol. 159 of Leibniz International Proceedings in Informatics (LIPIcs), p. 10:1–10:18
3. S. Ö. Stefänsson and B. Stufler. Geometry of Boltzmann outerplanar maps
   
   Mathematisches Forschungsinstitut Oberwolfach, Report No. 23/2018
4. B. Stufler. Local limits of large Galton-Watson trees rerooted at a random vertex
   
   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
5. K. Panagiotou, B. Stufler and K. Weller. Scaling limits of random graphs from subcritical classes: Extended abstract
   
   27th International Conference on Formal Power Series and Algebraic Combinatorics, DMTCS proc. FPSAC '15, p. 745–756, 2015.

Lecture notes and other informal notes:

1. B. Stufler. Lecture notes for my Introduction to random trees mini course at ISM Discovery School: Random trees, graphs and maps (UQAM, 2023)
   [notes] [slides (w/o videos)]
2. B. Stufler. Lecture notes for my Hopf Algebras course (University of Zurich, 2018)
   [pdf]