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Abstract : I investigate various instances of bifurcation in a random stationary environment. This is done for a model equation, with a bifurcation parameter fluctuating in space. The noise is either Gaussian or two states Poisson. I estimate then the order parameter as a function of a bifurcation parameter. This is mostly done by Lifshitz-tail type estimates on the linear part of the equation. However, near the threshold of instability in the absence of noise, this one-whatever small it is-becomes important and there the nonlinearity becomes crucial too.





Author: Y. Pomeau

Source: https://hal.archives-ouvertes.fr/



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