Related papers: From limit theorems to mixing limit theorems

We study compact hyperbolic surfaces and multiplication observables, establishing a large-scale analogue of Zelditch's quantum mixing theorem with hypotheses that hold for both arithmetic and Weil--Petersson random surfaces of large genus.…

We prove strengthenings of the Birkhoff Ergodic Theorem for weakly mixing and strongly mixing measure preserving systems. We show that our pointwise theorem for weakly mixing systems is strictly stronger than the Wiener-Wintner Theorem. We…

We prove functional limit theorems for dynamical systems in the presence of clusters of large values which, when summed and suitably normalised, get collapsed in a jump of the limiting process observed at the same time point. To keep track…

We prove non-trivial bounds for general bilinear forms in hyper-Kloosterman sums when the sizes of both variables may be below the P\'olya-Vinogradov range. We then derive applications to the second moment of holomorphic cusp forms twisted…

The paper is a sketch of systematic presentation of distributional limit theorems and their refinements for compound sums. When analyzing, e.g., ergodic semi-Markov systems with discrete or continuous time, this allows us to separate those…

In this paper we study decay of correlations and limit theorems for generalized baker's transformations. Our examples are piecewise non-uniformly hyperbolic maps on the unit square that posses two spatially separated lines of indifferent…

We prove quenched versions of a central limit theorem, a large deviations principle as well as a local central limit theorem for expanding on average cocycles. This is achieved by building an appropriate modification of the spectral method…

We consider the analogue of the quantum unique ergodicity conjecture for holomorphic Hecke eigenforms on compact arithmetic hyperbolic surfaces. We show that this conjecture follows from nontrivial bounds for Hecke eigenvalues summed over…

We apply a method inspired by Ratner's work on quantitative mixing for the geodesic flow (Ergod. Theory Dyn. Syst., 1987) and developed by Burger (Duke Math. J., 1990) to study ergodic integrals for horocycle flows. We derive an explicit…

We prove local limit theorems for a cocycle over a semiflow by establishing topological, mixing properties of the associated skew product semiflow. We also establish conditional rational weak mixing of certain skew product semiflows and…

Erdos-Renyi limit laws give the length scale of a time-window over which time-averages in Birkhoff sums have a non-trivial almost-sure limit. We establish Erdos-Renyi type limit laws for Holder observables on dynamical systems modeled by…

We consider Holder continuous linear cocycles over partially hyperbolic diffeomorphisms. For fiber bunched cocycles with one Lyapunov exponent we show continuity of measurable invariant conformal structures and sub-bundles. Further, we…

This work is a contribution to the study of the ergodic and stochastic properties of Z^d-periodic dynamical systems preserving an infinite measure. We establish functional limit theorems for natural Birkhoff sums related to local times of…

We prove several limit theorems for a simple class of partially hyperbolic fast-slow systems. We start with some well know results on averaging, then we give a substantial refinement of known large (and moderate) deviation results and…

The dynamics of one parameter diagonal group actions on finite volume homogeneous spaces has a partially hyperbolic feature. In this paper we extend the Liv\v{s}ic type result to these possibly noncompact and nonaccessible systems. We also…

Eagleson's Theorem asserts that, given a probability-preserving map, ifrenormalized Birkhoff sums of a function converge in distribution, thenthey also converge with respect to any probability measure which isabsolutely continuous with…

We prove combination theorems in the spirit of Klein and Maskit in the context of discrete convergence groups acting geometrically finitely on their limit sets. As special cases, we obtain combination theorems for geometrically finite…

We study mixing properties of generalized $T, T^{-1}$ transformation. We discuss two mixing mechanisms. In the case the fiber dynamics is mixing, it is sufficient that the driving cocycle is small with small probability. In the case the…

We prove a geometric criterion on a $\SL$-invariant ergodic probability measure on the moduli space of holomorphic abelian differentials on Riemann surfaces for the non-uniform hyperbolicity of the Kontsevich--Zorich cocycle on the real…

We consider generalized $(T, T^{-1})$ transformations such that the base map satisfies a multiple mixing local limit theorem and anticoncentration large deviation bounds and in the fiber we have $\mathbb{R}^d$ actions with $d=1$ or $2$…