Seminar "Interacting Random Systems"

Upcoming talks

• Wednesday, 27.09.2023, 11:30 (WIAS-405-406)
  Michiel Renger (TU Munich)
  Collisions in the exclusion process
  Abstract

  
  The simple symmetric exclusion process (SSEP) and a system of independent random walkers both converge to the same diffusion equation. To understand the difference, we count the number of times a SSEP particle would have jumped if the particles were independent, but did not jump because the target site was occupied. This number can also be interpreted as the number of times two SSEP particles collide. We show its hydrodynamic limit using Markov duality. In fact, we are interested in a whole zoo of related microscopic variables, and if time allows I will briefly talk about their large deviations.
  Ongoing work with Mario Ayala (TUM).

• Wednesday, 04.10.2023, 10:00 (WIAS-ESH)
  Subhro Ghosh (National University of Singapore)
  tba
• Wednesday, 04.10.2023, 11:30 (WIAS-405-406)
  Tiffany Y. Y. Lo (Uppsala University)
  tba
• Wednesday, 11.10.2023, 11:30 (WIAS-405-406)
  Bas Lodewijks (Augsburg University)
  Long-range first-passage percolation on the complete graph
  Abstract

  
  We consider first-passage percolation on the complete graph $K_n\,$, where vertices have a spatial position on the $d$-dimensional torus. For $\alpha\geq 0$, each edge $e$ in the graph is assigned an independent transmission time $T_e$, which is the product of a rate-one exponential random variable and the spatial length of the edge, raised to the power $\alpha$. When $\alpha=0$ we obtain the non-spatial case of first-passage percolation on the complete graph. We study the behaviour of the random metric induced by the transmission times in the case that $\alpha < d$. In particular, we investigate the typical distance, flooding time, and diameter of the graph, and obtain results akin to the well-established results for $\alpha=0$ case. If time permits, we shall also look into on-going work on competing long-range first-passage percolation, where two infections with possibly different transmission times occupy the vertices of the graph over time. Here, we investigate the possibility of coexistence, among other things.
  Mostly joint work with Remco van der Hofstad, and partially with Neeladri Maitra.

• Wednesday, 18.10.2023, 11:30 (WIAS-405-406)
  Simone Floreani (Oxford University)
  tba
• Wednesday, 01.11.2023, 11:30 (WIAS-405-406)
  Wolfgang König (WIAS and TU Berlin)
  tba
• Wednesday, 15.11.2023, 11:30 (WIAS-405-406)
  Elena Magnanini (WIAS Berlin)
  tba
• Wednesday, 29.11.2023, 11:30 (WIAS-405-406)
  Robert Patterson (WIAS Berlin)
  tba
• Wednesday, 13.12.2023, 11:30 (WIAS-405-406)
  Beatriz Salvador (Technical University of Lisbon)
  tba