Related papers: Decay of correlations for non-Holder observables

We consider a lattice of weakly coupled expanding circle maps. We construct, via a cluster expansion of the Perron-Frobenius operator, an invariant measure for these infinite dimensional dynamical systems which exhibits space-time-chaos.

We consider here a recent conjecture stating that correlation functions and tail probabilities of finite time Lyapunov exponents would have the same power law decay in weakly chaotic systems. We demonstrate that this conjecture fails for a…

We study local regularity properties of linear, non-uniformly parabolic finite-difference operators in divergence form related to the random conductance model on $\mathbb Z^d$. In particular, we provide an oscillation decay assuming only…

It was proven by Ures that $C^1$ diffeomorphism on three dimensional torus that is derived from Anosov admits a unique maximal measure. Here we show that the maximal measure has exponential decay of correlations for H\"older observables,…

We establish exponential decay in H\"older norm of transfer operators applied to smooth observables of uniformly and nonuniformly expanding semiflows with exponential decay of correlations.

We consider a finite number of orientation preserving $C^2$ interval diffeomorphisms and apply them randomly in such a way that the expected Lyapunov exponents at the boundary points are positive. We prove the exponential decay of…

Using perturbation theory, we explore the universal high momentum behavior of correlation functions of gauge invariant operators in planar noncommutative gauge theories. We find that the correlation functions are strongly enhanced when…

We argue that for generic systems close to a critical point, an extended Fluctuation-Dissipation relation connects the low frequency non-linear (cubic) susceptibility to the four-point correlation function. In glassy systems, the latter…

In this note, we study Luenberger-type full-state observers for nonlinear systems using contraction theory. We show that if the matrix measure of a suitably defined Jacobian matrix constructed from the dynamics of the system-observer…

We derive maps relating currents and their divergences in non-abelian U(N) noncommutative gauge theory with the corresponding expressions in the ordinary (commutative) description. For the U(1) theory, in the slowly-varying-field…

In this paper, we address the problem of hidden common variables discovery from multimodal data sets of nonlinear high-dimensional observations. We present a metric based on local applications of canonical correlation analysis (CCA) and…

The main result of this paper is a general central limit theorem for distributions defined by certain renewal type equations. We apply this to weakly self-avoiding random walks. We give good error estimates and Gaussian tail estimates which…

We introduce a new extragradient iterative process, motivated and inspired by [S. H. Khan, A Picard-Mann Hybrid Iterative Process, Fixed Point Theory and Applications, doi:10.1186/1687-1812-2013-69], for finding a common element of the set…

We prove a sharp criterion on the decay of the tension of almost harmonic maps from degenerating surfaces that ensures that such maps subconverge to a limiting object that is made up entirely of harmonic maps.

I present a new improved estimator for the correlation function of 2D nonlinear sigma models. Numerical tests for the 2D XY model and the 2D O(3)-invariant vector model were performed. For small physical volume, i.e. a lattice size small…

We study numerically the continuum limit corresponding to the non-trivial fixed point of Dyson's hierarchical model. We discuss the possibility of using the critical amplitudes as input parameters. We determine numerically the leading and…

We provide a generalization of the normal mode decomposition for non-symmetric or locality constrained situations. This allows for instance to locally decouple a bipartitioned collection of arbitrarily correlated oscillators up to…

Building upon previous works by Young, Chernov-Zhang and Bruin-Melbourne-Terhesiu, we present a general scheme to improve bounds on the statistical properties (in particular, decay of correlations, and rates in the almost sure invariant…

In this article we establish two fundamental results for the sublevel set persistent homology for stationary processes indexed by the positive integers. The first is a strong law of large numbers for the persistence diagram (treated as a…

In this paper, we study the non-self dual extended Harper's model with Liouvillean frequency. By establishing quantitative reducibility results together with the averaging method, we prove that the lengths of spectral gaps decay…