Davrbek Oltiboev

Linear response for random systems with a cusp

We study i.i.d.\ random compositions of cusp tent-like interval maps having a common cusp point and a common cusp value. For cusp exponents $-1<\beta<-\frac12$, we prove that the associated annealed transfer operators have a spectral gap on $W^{1,1}(I)$ and $W^{2,1}(I)$. For all sufficiently small perturbations of the...