Escape rates for noisy maps with anomalous prefactors

Abstract

The escape rate from a point attractor across an unstable fixed point is studied for a noisy map dynamics in 1 dimension. It is shown that for additive white noise xi with a distribution proportional to exp[-\xi\(alpha)], alpha > 1, the escape rate is dominated by an exponentially leading Arrhenius-like factor in the weak-noise limit. However, with the exception of Gaussian noise (alpha = 2), the pre-exponential contribution to the rate still depends more strongly than any power law on the noise strength.