Wednesday, 28 May 2025 at Augsburg University

Speakers:

• Inés Armendáriz (Buenos Aires)
• Michalis Loulakis (Athens)

Inés Armendáriz: Condensing zero range process

We prove a fluid limit for the coarsening phase of the condensing zero-range process on a finite number of sites. When time and occupation per site are linearly rescaled by the total number of particles, the evolution of the process is described by a piecewise linear trajectory in the simplex indexed by the sites. The linear coefficients are determined by the trace process of the underlying random walk on the subset of non-empty sites, and the trajectory reaches an absorbing configuration in finite time. We identify the set of absorbing configurations and characterize the absorbing boundaries.
Joint work with Johel Beltrán, Daniela Cuesta and Milton Jara.

Michalis Loulakis: Wasserstein spaces and error control in approximations by neural networks

We explore a connection between a weak topology on spaces of probability measures, a classical combinatorial problem in matching, and numerical schemes for the solution of PDEs by neural networks.