FWF Grant P34129

---

Project title: Growth models and quasi-random walks
Members of the project

• Yuwen Wang, PostDoc October 2021-March 2024.
• Robin Kaiser, PhD Student March 2022-August 2025.

Project description: We aim at working in an interdisciplinary field at the confluent of different branches of mathematics such as stochastics, combinatorics, graph theory, statistical physics with the plan of obtaining synergy effects. More precisely, we would like to understand how and why large-scale forms and complex patterns emerge from simple local rules.

Activities of the group: September 2021- September 2025

---

Publications of the group

1. Robin Kaiser and Ecaterina Sava-Huss: Random rotor walks and i.i.d. sandpiles on Sierpinski graphs. Statistics and Probability Letters 209 (2024).


2. Robin Kaiser and Ecaterina Sava-Huss: Scaling limit of the sandpile identity element on the Sierpinski gasket . Accepted for publication in From classical analysis to analysis on fractals: a tribute to Robert Strichartz, Volume 2, Applied and Numerical Harmonic Analysis, Birkhäuser; to appear (2024).


3. Uta Freiberg, Nico Heizmann, Robin Kaiser, Ecaterina Sava-Huss: Internal aggregation models with multiple sources and obstacle problems on Sierpinski gaskets. Journal of Fractal Geometry 11 (2024), no. 1/2, pp. 111–160.


4. Robin Kaiser, Ecaterina Sava-Huss, Yuwen Wang: Abelian sandpiles on Sierpinski gasket graphs. The Electronic Journal of Combinatorics 31(1) (2024), #P1.6


5. Konrad Kolesko and Ecaterina Sava-Huss: Limit theorems for discrete multitype branching processes counted with a characteristic. Stochastic Processes and their Applications 162 (2023), 49-75.


6. Daniela Bertacchi, Jürgen Kampf, Ecaterina Sava-Huss, Fabio Zucca
   An epidemic model in inhomogeneous environment.
   arXiv preprint. Markov Processes and Related Fields 28, Issue 3, 399-442 (2022).


7. Laurent Saloff-Coste and Yuwen Wang
   Random walks on finite nilpotent groups driven by long-jump measures.
   Electronic Journal of Probability 27, page 1-31, 2022.

Talks Ecaterina Sava-Huss (project leader)

• Abelian sandpile Markov chains. Geometric and Asymptotic Group Theory with Applications (GAGTA) 2023, ESI Vienna, Austria. July 17-21, 2023. invited speaker.
• Abelian sandpile Markov chains. Probability Colloquium Augsburg-Munich, LMU Munich, October 30, 2023.
• Probability seminar Vienna, January 11, 2023. Talk: Aggregation models with multiple sources on fractal graphs.
• Invited speaker colloquium: Kolloquium aus Anlass der Emeritierung von Wolfgang Woess, TU Graz, Austria. October 24, 2022. Talk: Aggregation models with multiple sources on fractal graphs.
• Contributed talk: Austrian stochastics days 2022; University of Vienna, September 8-9, 2022. Talk: Sandpiles on the gasket:
• Invited speaker: 7th Cornell Conference on Analysis, Probability, and Mathematical Physics on Fractals, USA , June 2022. Talk: Sandpiles on the gasket: many questions & few answers.
• Keynote speaker: Second Austrian Day of women in mathematics, online meeting, February 02, 2022. Talk: Particles moving randomly or not?
• Invited seminar talk: Department of Mathematics, Chemnitz University of Technology, Germany; November 2021. Talk: Combinatorial and probabilistic growth models
• Contributed talk: DMV-ÖMG Annual Conference 2021; University of Passau, September 27 - October 1, 2021 (virtual talk). Talk: Probabilistic and combinatorial growth models.
• Contributed talk: German Probability & Statistics Days; Mannheim, September 27 - October 1, 2021 (virtual talk). Talk: Interpolating between random walk and rotor walk.
• Keynote speaker: talk at Austrian Stochastics Days 2021, September 9-10, Leoben (Austria), 2021. Talk: Combinatorial and probabilistic growth models.

Research visits and other project related activities

• 02/2023 Robin Kaiser visited the research project partners (Uta Freiberg and Nico Heizmann) at Chemnitz University of Technology.
• 07-08/2022 Yuwen Wang visited Cornell University for the Probability Summer School and for working with research partners Laurent Saloff-Coste and Lionel Levine.
• 07/2022 Robin Kaiser visited the research project partners (Uta Freiberg and Nico Heizmann) at Chemnitz University of Technology.