Workshop Women in Probability 2019
The scientific program is organized by Noam Berger, Diana Conache, Nina Gantert, Silke Rolles and Sabine Jansen (LMU). This conference is supported by the "Women for Math Science Program" at Technische Universität München.
There is no conference fee and there are no gender restrictions on the audience, everybody is welcome to attend.
For hotel reservations, please contact Silvia Schulz.
Location and dates
Friday afternoon, 31th May, and Saturday morning, 1th June 2019, at Zentrum Mathematik, Technische Universität München.
- Luisa Andreis (Weierstraß-Institut)
- Gioia Carinci (Delft University of Technology)
- Hanna Döring (Universität Osnabrück)
- Lisa Hartung (Johannes Gutenberg-Universität Mainz)
- Cecile Mailler (University of Bath)
- Eveliina Peltola (University of Geneva)
- Elena Pulvirenti (Universität Bonn)
- Ecaterina Sava-Huss (Graz University of Technology)
Friday, May 31th, 2019:
- 14:00-14:45 Luisa Andreis: TBA
- 15:00-15:45 Eveliina Peltola: Crossing probabilities of multiple Ising interfaces
- 15:45-16:15 Coffee Break
- 16:15-17:00 Lisa Hartung: TBA
- 17:15-18:00 Ecaterina Sava-Huss: Aggregation models based on random walks and rotor walks
We will go for dinner after the talks.
Saturday, June 1th, 2019:
- 09:00-09:45 Cecile Mailler: The monkey walk: A random walk with random reinforced relocations and fading memory
- 09:55-10:40 Gioia Carinci: Inclusion process, sticky brownian motion and condensation
- 10:40-11:00 Coffee Break
- 11:00-11:45 Hanna Doering: Limit theorems in dynamic random networks
- 11:55-12:40 Elena Pulvirenti: TBA
Titles and abstracts
- Luisa Andreis: TBA
- Gioia Carinci: Inclusion process, sticky brownian motion and condensation.
Abstract: The inclusion process is an interacting particle system modeling the motion of agents diffusing with an attractive interaction. I will discuss its behavior in a suitable condensation regime where the attractive part of the dynamics is predominant. In particular an explicit formula is obtained for expectation and variance of the fluctuation density field. This result shows, from a microscopic point of view, the formation of a condensed state where particles pile up. The proof is based on duality and the study of the two-particle dual process that is proved to converge to sticky Brownian particles. Joint work with C. Giardina, F. Redig
- Hanna Döring: Limit theorems in dynamic random networks
Abstract: Many real world phenomena can be modelled by dynamic random networks. We will focus on preferential attachment models where the networks grow node by node and edges with the new vertex are added randomly depending on a sublinear function of the degree of the older vertex. Using Stein’s method provides rates of convergence for the total variation distance between the evolving degree distribution and an asymptotic power-law distribution as the number of vertices tends to infinity. This is a joint work with Carina Betken and Marcel Ortgiese.
- Lisa Hartung: TBA
- Cecile Mailler: The monkey walk: A random walk with random reinforced relocations and fading memory
Abstract: In this joint work with Gerónimo Uribe-Bravo, we prove and extend results from the physics literature about a random walk with random reinforced relocations. The "walker" evolves in $\mathbb Z^d$ or $\mathbb R^d$ according to a Markov process, except at some random jump-times, where it chooses a time uniformly at random in its past, and instatnly jumps to the position it was at that random time. This walk is by definition non-Markovian, since the walker needs to remember all its past. Under moment conditions on the inter-jump-times, and provided that the underlying Markov process verifies a distributional limit theorem, we show a distributional limit theorem for the position of the walker at large time. The proof relies on exploiting the branching structure of this random walk with random relocations; we are able to extend the model further by allowing the memory of the walker to decay with time.
- Eveliina Peltola: Crossing probabilities of multiple Ising interfaces
Abstract: I discuss crossing probabilities of multiple interfaces in the critical Ising model with alternating boundary conditions. In the scaling limit, they are conformally invariant expressions given by so-called pure partition functions of multiple SLE(kappa) with kappa=3. I also describe analogous results for critical percolation and the Gaussian free field. This is joint work with Hao Wu (Yau Center / Tsinghua University).
- Elena Pulvirenti: TBA
- Ecaterina Sava-Huss: Aggregation models based on random walks and rotor walks
Abstract: In this talk, I will focus on the behavior of the following cluster growth models: internal DLA, the rotor model, and the divisible sandpile model. These models can be run on any infinite graph, and they are based on particles moving around according to some rule (that can be either random or deterministic) and aggregating. Describing the limit shape of the cluster these particles produce is one of the main questions one would like to answer. For some of the models, the fractal nature of the cluster is, from the mathematical point of view, far away from being understood. I will give an overview on the known limit shapes for the above mentioned growth models; in particular I will present a limit shape universality result on the Sierpinski gasket graph, and conclude with some open questions. The results are based on collaborations with J. Chen, W. Huss, and A. Teplyaev.