Communications in Mathematical Sciences

Volume 8 (2010)

Number 2

Special Issue on the Occasion of Andrew Majda’s Sixtieth Birthday: Part II

Application of the stochastic mode-reduction strategy and a priori prediction of symmetry breaking in stochastic systems with underlying symmetry

Pages: 393 – 408



N. Barlas

I. Timofeyev


We consider application of the stochastic mode-reduction strategy to a particular class of coupled models where a part of self-interactions of the slow variables is given by a rotationally invariant gradient system. The stochastic mode-reduction strategy is utilized to derive stochastic reduced models which yield a simple description of the phenomena resulting from breaking the original rotational symmetry. It is demonstrated that the direction of the symmetry breaking can be predicted a priori without any knowledge of the statistical behavior of the fast modes.


Stochastic modeling; mode reduction; symmetry breaking

2010 Mathematics Subject Classification

60H10, 60H35, 65C30

Full Text (PDF format)