Related papers: Quantitative recurrence statistics and convergence…
In this paper, we consider the convergence rate with respect to Wasserstein distance in the invariance principle for deterministic nonuniformly hyperbolic systems, where both discrete time systems and flows are included. Our results apply…
Using a renormalization approach, we study the asymptotic limit distribution of the maximum value in a set of independent and identically distributed random variables raised to a power q(n) that varies monotonically with the sample size n.…
We provide formulas to compute the coefficients entering the affine scaling needed to get a non-degenerate function for the asymptotic distribution of the maxima of some kind of observable computed along the orbit of a randomly perturbed…
We consider invertible discrete-time dynamical systems having a hyperbolic product structure in some region of the phase space with infinitely many branches and variable recurrence time. We show that the decay of correlations of the SRB…
Recurrent temporal dynamics is a phenomenon observed frequently in high-dimensional complex systems and its detection is a challenging task. Recurrence quantification analysis utilizing recurrence plots may extract such dynamics, however it…
We analyze in detail, beyond the usual scaling hypothesis, the finite-size convergence of static quantities toward the thermodynamic limit. In this way we are able to obtain sequences of pseudo-critical points which display a faster…
The rate of uniform convergence in extreme value statistics is non-universal and can be arbitrarily slow. Further, the relative error can be unbounded in the tail of the approximation, leading to difficulty in extrapolating the extreme…
We deal with a generalized statistical description of nonequilibrium complex systems based on least biased distributions given some prior information. A maximum entropy principle is introduced that allows for the determination of the…
We establish a theory for multivariate extreme value analysis of dynamical systems. Namely, we provide conditions adapted to the dynamical setting which enable the study of dependence between extreme values of the components of…
In this paper we study the distribution of hitting and return times for observations of dynamical systems. We apply this results to get an exponential law for the distribution of hitting and return times for rapidly mixing random dynamical…
Recurrence is a fundamental property of dynamical systems, which can be exploited to characterise the system's behaviour in phase space. A powerful tool for their visualisation and analysis called recurrence plot was introduced in the late…
Multivariate extreme value statistical analysis is concerned with observations on several variables which are thought to possess some degree of tail-dependence. In areas such as the modeling of financial and insurance risks, or as the…
We show that for systems that allow a Young tower construction with polynomially decaying correlations the return times to metric balls are in the limit Poisson distributed. We also provide error terms which are powers of logarithm of the…
For a measure preserving dynamical system $(\mathcal{X},f, \mu)$, we consider the time series of maxima $M_n=\max\{X_1,\ldots,X_n\}$ associated to the process $X_n=\phi(f^{n-1}(x))$ generated by the dynamical system for some observable…
Mixed modeling of extreme values and random effects is relatively unexplored topic. Computational difficulties in using the maximum likelihood method for mixed models and the fact that maximum likelihood method uses available data and does…
We consider stationary stochastic processes arising from dynamical systems by evaluating a given observable along the orbits of the system. We focus on the extremal behaviour of the process, which is related to the entrance in certain…
We show that the dynamics of generic quantum systems concentrate around their equilibrium value when measuring at arbitrary times. This means that the probability of finding them away from equilibrium is exponentially suppressed, with a…
It has been shown that sufficiently well mixing dynamical systems with positive entropy have extreme value laws which in the limit converge to one of the three standard distributions known for i.i.d. processes, namely Gumbel, Fr\'echet and…
We analyze general enough models of repeated indirect measurements in which a quantum system interacts repeatedly with randomly chosen probes on which Von Neumann direct measurements are performed. We prove, under suitable hypotheses, that…
We develop and generalize the theory of extreme value for non-stationary stochastic processes, mostly by weakening the uniform mixing condition that was previously used in this setting. We apply our results to non-autonomous dynamical…