Eindhoven University of Technology (TU/e)

I have had my results for a long time: But I do not yet know how I am to arrive at them

*Carl Friedrich Gauss (1777—1855, German mathematician and physicist)*

Here, you find information on research activities, publications, and members within the Vidi project:

Evolution equations in spaces of measures describe a wide variety of natural phenomena. The theory for such evolutions has seen tremendous growth in the last decades, of which resulted in (1) the metric space theory for gradient flows, and (2) the theory of rate-independent systems for analysing variational evolutions—evolutions driven by one or more energies/entropies.

While these theories have allowed for massive development of variational evolutions in a certain direction—gradient flows with homogeneous dissipation—physics and large-deviation theory suggest the study of **generalised gradient flows**—gradient flows with non-homogeneous dissipation—which are not covered in either theories.

In this project, we develop a theory of **dynamical-variational transport costs (DVTs)**, a class of large-deviation inspired functionals that provide a variational generalisation of a zoo of existing transport distances. DVTs generate non-homogeneous generalisations of length spaces that will be used to extend metric-space techniques to general length spaces, thereby allowing a variational framework for (A) generalised gradient flows to be rigorously investigated, and (B) the multiscale analysis of such evolutions used in the development of numerical schemes.

- Jasper Hoeksema and Oliver Tse. Generalized gradient structures for measure-valued population dynamics and their large-population limit (arXiv:2207.00853)
- Anastasiia Hraivoronska and Oliver Tse. Diffusive limit of random walks on tessellations via generalized gradient flows (arXiv:2202.06024)
- Simone Fagioli and Oliver Tse. On gradient flow and entropy solutions for nonlocal transport equations with nonlinear mobility

Nonlinear Analysis, 2022. (arXiv:2105.11389) - Mark A. Peletier, Riccarda Rossi, Giuseppe Savaré and Oliver Tse. Jump processes as Generalized Gradient Flows

Calculus of Variations and Partial Differential Equations, 2022. (arXiv:2006.10624) - Bastian Hilder, Mark A. Peletier, Upanshu Sharma and Oliver Tse. An inequality connecting entropy distance, Fisher Information and large deviations

Stochastic Processes and their Applications, 2019. (arXiv:1812.04358)

- Jasper Hoeksema, PhD Student
- Anastasiia Hraivoronska, PhD Student

- Simone Fagioli, University of L'Aquila
- Bastian Hilder, University of Stuttgart
- Mark A. Peletier, Eindhoven University of Technology
- Riccarda Rossi, University of Brescia
- Giuseppe Savaré, Bocconi University
- Upanshu Sharma, Freie Universität Berlin