2024
http://publications.mfo.de/handle/mfo/4132
Tue, 18 Jun 2024 00:00:54 GMT2024-06-18T00:00:54ZRandomness is Natural - an Introduction to Regularisation by Noise
http://publications.mfo.de/handle/mfo/4146
Randomness is Natural - an Introduction to Regularisation by Noise
Djurdjevac, Ana; Elad Altman, Henri; Rosati, Tommaso
Differential equations make predictions on the future state of a system given the present. In order to get a sensible prediction, sometimes it is necessary to include randomness in differential equations, taking microscopic effects into account. Surprisingly, despite the presence of randomness, our probabilistic prediction of future states is stable with respect to changes in the surrounding environment, even if the original prediction was unstable. This snapshot will unveil the core mathematical mechanism underlying this "regularisation by noise" phenomenon.
Wed, 22 May 2024 00:00:00 GMThttp://publications.mfo.de/handle/mfo/41462024-05-22T00:00:00ZDjurdjevac, AnaElad Altman, HenriRosati, TommasoDifferential equations make predictions on the future state of a system given the present. In order to get a sensible prediction, sometimes it is necessary to include randomness in differential equations, taking microscopic effects into account. Surprisingly, despite the presence of randomness, our probabilistic prediction of future states is stable with respect to changes in the surrounding environment, even if the original prediction was unstable. This snapshot will unveil the core mathematical mechanism underlying this "regularisation by noise" phenomenon.Waves and Incidences
http://publications.mfo.de/handle/mfo/4133
Waves and Incidences
Yung, Po-Lam
The wave equation in Euclidean spaces describes many natural phenomena such as sound, light, or water waves. We explore how its solutions are related to the geometric problem of how long thin cylinders can intersect each other and discuss a related open problem.
Tue, 09 Apr 2024 00:00:00 GMThttp://publications.mfo.de/handle/mfo/41332024-04-09T00:00:00ZYung, Po-LamThe wave equation in Euclidean spaces describes many natural phenomena such as sound, light, or water waves. We explore how its solutions are related to the geometric problem of how long thin cylinders can intersect each other and discuss a related open problem.