Stochastic Analysis Seminar – Nicolas Perkowski (Institut für Mathematik)

It is a classical result that sufficiently strong noise can wipe out deterministic bifurcations: instead of new stable equilibria appearing, randomness can enforce a unique invariant regime (in the spirit of Crauel-Flandoli). More recently, however, a more subtle picture has emerged. Even when the long-time stationary behaviour looks “noise-stabilized,” one can still observe qualitative bifurcation-like signatures on finite time horizons, for example through random finite-time growth rates (as in work of Callaway et al, and Blessing et al). In my talk I will show that the two-dimensional singular $\Phi^4_2$ equation behaves in an even more radical way at a pitchfork bifurcation and renormalization eliminates even these finite-time bifurcation signatures. This is joint work with Alexandra Blessing Neamțu and Chara Zhu.