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Items filtered by date: Sunday, 16 October 2022

 Speaker: Pierre-Emmanuel Jabin (Pennsylvania State University)

We introduce a novel approach to the mean-field limit of stochastic systems of interacting particles, leading to the first ever derivation of the mean-field limit to the Vlasov-Poisson-Fokker-Planck system for plasmas in dimension 2 together with a partial result in dimension 3. The method is broadly compatible with second order systems that lead to kinetic equations and it relies on novel estimates on the BBGKY hierarchy. By taking advantage of the diffusion in velocity, those estimates bound weighted L p norms of the marginals or observables of the system uniformly in the number of particles. This allows to treat very singular interaction kernels between the particles, including repulsive Poisson interactions. This is a joint work with D. Bresch and J. Soler. 
 

Time: December 2, 2022 2:30pm-3:30pm
Location: Virtually via Zoom
Host: Changhui Tan

Published in ACM Seminar

 Speaker: Amir Sagiv (Columbia University)

In many scientific areas, deterministic models (e.g., differential equations) use numerical parameters. Often, such parameters might be uncertain or noisy. A more honest model should therefore provide a statistical description of the quantity of interest. Underlying this numerical analysis problem is a fundamental question - if two "similar" functions push-forward the same measure, would the new resulting measures be close, and if so, in what sense? We will first show how the probability density function (PDF) of the quantity of interest can be approximated. We will then discuss how, through the lense of the Wasserstein-distance, our problem yields a simpler and more robust theoretical framework.

Finally, we will take a steep turn to a seemingly unrelated topic: the computational sampling problem. In particular, we will discuss the emerging class of sampling-by-transport algorithms, which to-date lacks rigorous theoretical guarantees. As it turns out, the mathematical machinery developed in the first half of the talk provides a clear avenue to understand this latter class of algorithms. 
 

Time: November 11, 2022 2:30pm-3:30pm
Location: Virtually via Zoom
Host: Wolfgang Dahmen

Published in ACM Seminar