English
Related papers

Related papers: Nonconventional Large Deviations Theorems

200 papers

The problem of (pathwise) large deviations for conditionally continuous Gaussian processes is investigated. The theory of large deviations for Gaussian processes is extended to the wider class of random processes -- the conditionally…

Probability · Mathematics 2019-02-07 Barbara Pacchiarotti , Alessandro Pigliacelli

Large deviation theory quantifies the occurence of events that deviate from the average behavior of a system. Such events arise from non-typical trajectories of the dynamics. In this note we derive the time evolution of these rare…

Statistical Mechanics · Physics 2012-12-11 David Andrieux

Limit theorems, including the large deviation principle, are established for random point processes (fields), which describe the position distributions of the perfect boson gas in the regime of the Bose-Einstein condensation. We compare…

Mathematical Physics · Physics 2015-05-14 Hiroshi Tamura , Valentin Zagrebnov

The nonlinear Markov processes are the measure-valued dynamical systems which preserve positivity. They can be represented as the law of large numbers limits of general Markov models of interacting particles. In physics, the kinetic…

Chemical Physics · Physics 2015-09-28 A. N. Gorban , V. N. Kolokoltsov

For sequences of non-lattice weakly dependent random variables, we obtain asymptotic expansions for Large Deviation Principles. These expansions, commonly referred to as strong large deviation results, are in the spirit of Edgeworth…

Probability · Mathematics 2020-03-10 Kasun Fernando , Pratima Hebbar

A general sufficient condition for the convergence of subsequences of solutions of non-autonomous, nonlinear difference equations and systems is obtained. For higher order equations the delay sizes and patterns play essential roles in…

Dynamical Systems · Mathematics 2017-07-25 H. Sedaghat

This paper develops central limit theorems (CLT's) and large deviations results for additive functionals associated with reflecting diffusions in which the functional may include a term associated with the cumulative amount of boundary…

Probability · Mathematics 2014-07-10 Peter W. Glynn , Rob J. Wang

We obtain functional central limit theorems for both discrete time expressions of the form $1/\sqrt{N}\sum_{n=1}^{[Nt]}(F(X(q_1(n)),\ldots, X(q_{\ell}(n)))-\bar{F})$ and similar expressions in the continuous time where the sum is replaced…

Probability · Mathematics 2014-02-26 Yuri Kifer , S. R. S. Varadhan

A large deviation function mathematically characterizes the statistical property of atypical events. Recently, in non-equilibrium statistical mechanics, large deviation functions have been used to describe universal laws such as the…

Statistical Mechanics · Physics 2012-04-26 Shin-ichi Sasa

For Markov processes evolving on multiple time-scales a combination of large component scalings and averaging of rapid fluctuations can lead to useful limits for model approximation. A general approach to proving a law of large numbers to a…

Probability · Mathematics 2020-12-29 Lea Popovic

We investigate superdiffusion for stochastic processes generated by nonuniformly hyperbolic system models, in terms of the convergence of rescaled distributions to the normal distribution following the abnormal central limit theorem, which…

Dynamical Systems · Mathematics 2017-09-05 Luke Mohr , Hong-Kun Zhang

Using a generalisation of the detailed balance for systems maintained out of equilibrium by contact with 2 reservoirs at unequal temperatures or at unequal densities, we recover the fluctuation theorem for the large deviation funtion of the…

Statistical Mechanics · Physics 2009-11-13 T. Bodineau , B. Derrida

We study the large deviations principle for one dimensional, continuous, homogeneous, strong Markov processes that do not necessarily behave locally as a Wiener process. Any strong Markov process $X_{t}$ in $\mathbb{R}$ that is continuous…

Probability · Mathematics 2011-07-19 Konstantinos Spiliopoulos

We continue the investigation of the spectral theory and exponential asymptotics of Markov processes, following Kontoyiannis and Meyn (2003). We introduce a new family of nonlinear Lyapunov drift criteria, characterizing distinct subclasses…

Probability · Mathematics 2007-05-23 Ioannis Kontoyiannis , S. P. Meyn

This article is devoted to level-1 large deviation properties in some nonuniformly hyperbolic systems via Pesin theory. In particular, our result can be applied to the nonuniformly hyperbolic diffeomorphisms described by Katok and several…

Dynamical Systems · Mathematics 2014-12-03 Zheng Yin , Ercai Chen

We consider a two-dimensional Hamiltonian system perturbed by a small diffusion term, whose coefficient is state-dependent and non-degenerate. As a result, the process consists of the fast motion along the level curves and slow motion…

Probability · Mathematics 2022-05-24 Shuo Yan

Ordinary differential equations obtained as limits of Markov processes appear in many settings. They may arise by scaling large systems, or by averaging rapidly fluctuating systems, or in systems involving multiple time-scales, by a…

Probability · Mathematics 2014-03-24 Hye-Won Kang , Thomas G. Kurtz , Lea Popovic

The theory of large deviations is concerned with the exponential decay of probabilities of large fluctuations in random systems. These probabilities are important in many fields of study, including statistics, finance, and engineering, as…

Statistical Mechanics · Physics 2009-08-20 Hugo Touchette

The large deviations properties of trajectory observables for chaotic non-invertible deterministic maps as studied recently by N. R. Smith, Phys. Rev. E 106, L042202 (2022) and by R. Gutierrez, A. Canella-Ortiz, C. Perez-Espigares,…

Statistical Mechanics · Physics 2024-01-30 Cecile Monthus

Understanding transport processes in complex nanoscale systems, like ionic conductivities in nanofluidic devices or heat conduction in low dimensional solids, poses the problem of examining fluctuations of currents within nonequilibrium…

Mesoscale and Nanoscale Physics · Physics 2021-08-04 David T. Limmer , Chloe Y. Gao , Anthony R. Poggioli