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We present a large deviation property for the pattern statistics representing the number of occurrences of a symbol in words of given length generated at random according to a rational stochastic model. The result is obtained assuming that…

Probability · Mathematics 2023-06-14 Massimiliano Goldwurm , Marco Vignati

We prove pathwise large deviation principles of slow variables in slow-fast systems in the limit of time-scale separation tending to infinity. In the limit regime we consider, the convergence of the slow variable to its deterministic limit…

Probability · Mathematics 2020-11-25 Richard C. Kraaij , Mikola C. Schlottke

Limit theorems for a linear dynamical system with random interactions are established. These theorems enable us to characterize the dynamics of a large complex system in details and assess whether a large complex system is stable or…

Mathematical Physics · Physics 2011-11-10 J. F. Feng , M. Shcherbina , B. Tirozzi

We consider perturbations of interval maps with indifferent fixed points, which we refer to as wobbly interval intermittent maps, for which stable laws for general H\"older observables fail. We obtain limit laws for such maps and H\"older…

Dynamical Systems · Mathematics 2020-11-24 Douglas Coates , Mark Holland , Dalia Terhesiu

We obtain large and moderate deviation estimates, as well as concentration inequalities, for a class of nonuniformly expanding maps with stretched exponential decay of correlations. In the large deviation regime, we also exhibit examples…

Probability · Mathematics 2022-01-26 C Cuny , J Dedecker , F Merlevède

We introduce orthogonal ring patterns in the 2-sphere and in the hyperbolic plane, consisting of pairs of concentric circles, which generalize circle patterns. We show that their radii are described by a discrete integrable system. This is…

Metric Geometry · Mathematics 2024-10-14 Alexander I. Bobenko

This work studies a two-time-scale functional system given by two jump-diffusions under the scale separation by a small parameter $\varepsilon \rightarrow 0$. The coefficients of the equations that govern the dynamics of the system depend…

Probability · Mathematics 2022-07-15 André de Oliveira Gomes , Pedro Catuogno

Large deviations in chaotic dynamics have potentially significant and dramatic consequences. We study large deviations of series of finite lengths $N$ generated by chaotic maps. The distributions generally display an exponential decay with…

Chaotic Dynamics · Physics 2022-10-21 Naftali R. Smith

For one-dimensional Jump-Drift and Jump-Diffusion processes converging towards some steady state, the large deviations of a long dynamical trajectory are described from two perspectives. Firstly, the joint probability of the empirical…

Statistical Mechanics · Physics 2021-08-17 Cecile Monthus

We present a general theory to quantify the uncertainty from imposing structural assumptions on the second-order structure of nonstationary Hilbert space-valued processes, which can be measured via functionals of time-dependent spectral…

Statistics Theory · Mathematics 2023-09-19 Anne van Delft , Holger Dette

We establish the large deviation principle for a topological Markov shift over infinite alphabet which satisfies strong combinatorial assumptions called ``finite irreducibility'' or ``finite primitiveness''. More precisely, we assume the…

Dynamical Systems · Mathematics 2019-03-19 Hiroki Takahasi

We consider a general class of statistical mechanical models of coherent structures in turbulence, which includes models of two-dimensional fluid motion, quasi-geostrophic flows, and dispersive waves. First, large deviation principles are…

Probability · Mathematics 2007-05-23 R. S. Ellis , K. Haven , B. Turkington

We present an algorithm to evaluate the large deviation functions associated to history-dependent observables. Instead of relying on a time discretisation procedure to approximate the dynamics, we provide a direct continuous-time algorithm,…

Statistical Mechanics · Physics 2007-12-03 Vivien Lecomte , Julien Tailleur

We cosider random dynamical systems with randomly chosen jumps. The choice of deterministic dynamical system and jumps depends on a position. We proove the existence of an exponentially attractive invariant measure and the strong law of…

Probability · Mathematics 2013-04-26 K. Horbacz , M. Ślęczka

We show that accelerated gradient descent, averaged gradient descent and the heavy-ball method for non-strongly-convex problems may be reformulated as constant parameter second-order difference equation algorithms, where stability of the…

Machine Learning · Statistics 2015-04-08 Nicolas Flammarion , Francis Bach

The correct computation of orbits of discrete dynamical systems on the interval is considered. Therefore, an arbitrary-precision floating-point approach based on automatic error analysis is chosen and a general algorithm is presented. The…

Numerical Analysis · Computer Science 2015-03-13 Christoph Spandl

We determine limiting equations for large asymmetric `spin glass' networks. The initial conditions are not assumed to be independent of the disordered connectivity: one of the main motivations for this is that allows one to understand how…

Disordered Systems and Neural Networks · Physics 2024-02-13 James MacLaurin , Moshe Silverstein , Pedro Vilanova

In the framework of Harnack type Dirichlet forms, we prove a large deviation principle for the asymptotics of reversible Markov processes with rate function given by the energy of the paths.

Probability · Mathematics 2009-07-28 Ann-Kathrin Jarecki

We study temporally persistent and spatially extended extreme events of temperature anomalies, i.e. heat waves and cold spells, using large deviation theory. To this end, we consider a simplified yet Earth-like general circulation model of…

Statistical Mechanics · Physics 2019-05-22 Vera Melinda Galfi , Valerio Lucarini , Jeroen Wouters

Volatilities, in high-dimensional panels of economic time series with a dynamic factor structure on the levels or returns, typically also admit a dynamic factor decomposition. We consider a two-stage dynamic factor model method recovering…

Econometrics · Economics 2022-02-03 Matteo Barigozzi , Marc Hallin