Monday, 28 April 2025 at LMU Munich

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Speakers:

• Perla Sousi (Cambridge)
• Sebastian Andres (Braunschweig)

Perla Sousi: t.b.a.

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Sebastian Andres:?Scaling limit of the harmonic crystal with random conductances

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In this talk we consider discrete Gaussian free fields with ergodic random conductances on ?^d, d ≥ 2, where the conductances are possibly unbounded but satisfy a moment condition. As our main result, we show that, for almost every realisation of the environment, the rescaled field converges in law towards a continuous Gaussian field. We also present a scaling limit for the covariances of the field. To obtain the latter, we establish a quenched local limit theorem for the Green's function of the associated random walk among random conductances with Dirichlet boundary conditions. This talk is based on a joint work with Martin Slowik and Anna-Lisa Sokol.

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Wednesday, 28 May 2025 at Augsburg University

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Speakers:

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

Inés Armendáriz: t.b.a.

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

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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.

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