5 papers
Martingale Methods for Maximal Large Deviations and Young Towers
José F. Alves, João S. Matias, Ian Melbourne
We develop a martingale approximation framework yielding quantitative maximal large deviations estimates for invertible dynamical systems. From suitable decay of correlations, we d…
Nonstandard functional central limit theorem for nonuniformly hyperbolic dynamical systems, including Bunimovich stadia
Yuri Lima, Carlos Matheus, Ian Melbourne
We consider a class of nonuniformly hyperbolic dynamical systems with a first return time satisfying a central limit theorem (CLT) with nonstandard normalisation .…
Superdiffusive central limit theorems for geodesic flows on nonpositively curved surfaces
Yuri Lima, Carlos Matheus, Ian Melbourne
We prove a nonstandard central limit theorem and weak invariance principle, with superdiffusive normalisation , for geodesic flows on a class of nonpositively curv…
Wasserstein convergence rates in the invariance principle for nonuniformly hyperbolic flows
Ian Melbourne, Zhe Wang
We obtain -Wasserstein convergence rates in the invariance principle for nonuniformly hyperbolic flows, where depends on the degree of nonuniformity. Utilizing a marting…
Superdiffusive limits beyond the Marcus regime for deterministic fast-slow systems
Ilya Chevyrev, Alexey Korepanov, Ian Melbourne
We consider deterministic fast-slow dynamical systems of the form \[ x_{k+1}^{(n)} = x_k^{(n)} + n^{-1} A(x_k^{(n)}) + n^{-1/α} B(x_k^{(n)}) v(y_k), \quad y_{k+1} = Ty_k, \] where…