Faculty of Mathematics
Collaborative Research Centre 701
Spectral Structures and Topological Methods in Mathematics

# Project A3

## Stochastic dynamics and bifurbications

Principal Investigator(s) Other Investigators

## Summary:

The project addresses central questions about stochastic processes and their dynamics in various random environments, including noise-induced transitions for diffusions evolving in an environment subject to slow change and random perturbations, metastability for coupled diffusion processes, scenery reconstruction from a record of colourings observed along a random walk path, and the problem of optimal alignment of random strings. Stochastic processes in random media have been a very active area of research in the past decade (see e.g.Bolthausen and Sznitman, 2002) as has the area of random dynamical systems (Arnold, 1998). Yet, the theory of bifurcations in random dynamical systems is still in its infancy.

This project continues the successful work of the project Stochastic processes in random media under the direction of Friedrich Götze and Silke Rolles.

 13024 Uniform propagation of chaos for a class of inhomogeneous diffusions PDF | PS.GZ 12074 On the noise-induced passage through an unstable periodic orbit II: General case PDF | PS.GZ 12047 Estimates for the rate of strong approximation in Hilbert space PDF | PS.GZ 12008 Sharp estimates for metastable lifetimes in parabolic SPDEs: Kramers’ law and beyond PDF | PS.GZ 11092 Self-stabilizing processes in multi-wells landscape in $\mathbb{R}^d$ - Invariant probabilities PDF | PS.GZ 11091 Exit problem of McKean-Vlasov diffusions in convex landscape PDF | PS.GZ 11090 Self-stabilizing processes in multi-wells landscape in $\mathbb{R}^d$ - Convergence PDF | PS.GZ 11065 McKean-Vlasov diffusions: from the asynchronization to the synchronization PDF | PS.GZ 11063 On the functions counting walks with small steps in the quarter plane PDF | PS.GZ 11039 Random walks reaching against all odds the other side of the quarter plane PDF | PS.GZ