Related papers: A basic introduction to large deviations: Theory, …
We consider a typical learning problem of point estimations for modeling of nonlinear functions or dynamical systems in which generalization, i.e., verifying a given learned model, can be embedded as an integral part of the learning process…
Information thermodynamics provides a framework for studying the effect of feedback loops on entropy production. It has enabled the understanding of novel thermodynamic systems such as the information engine which can be seen as a modern…
The large deviation principle is proved for a class of $L^2$-valued processes that arise from the coarse-graining of a random field. Coarse-grained processes of this kind form the basis of the analysis of local mean-field models in…
This paper is concerned with the general theme of relating the Large Deviation Principle (LDP) for the invariant measures of stochastic processes to the associated sample path LDP. It is shown that if the sample path deviation function…
We analyse large deviations of time-averaged quantities in stochastic processes with long-range memory, where the dynamics at time t depends itself on the value q_t of the time-averaged quantity. First we consider the elephant random walk…
The concept of random dynamical system is a comparatively recent development combining ideas and methods from the well developed areas of probability theory and dynamical systems. Due to our inaccurate knowledge of the particular physical…
Markov processes restarted or reset at random times to a fixed state or region in space have been actively studied recently in connection with random searches, foraging, and population dynamics. Here we study the large deviations of…
We consider the effects of long-range temporal correlations in many-particle systems, focusing particularly on fluctuations about the typical behaviour. For a specific class of memory dependence we discuss the modification of the large…
From the sampling of data to the initialisation of parameters, randomness is ubiquitous in modern Machine Learning practice. Understanding the statistical fluctuations engendered by the different sources of randomness in prediction is…
We propose a method to calculate the large deviations of current fluctuations in a class of stochastic particle systems with history-dependent rates. Long-range temporal correlations are seen to alter the speed of the large deviation…
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…
We present an analytical technique to compute the probability of rare events in which the largest eigenvalue of a random matrix is atypically large (i.e.\ the right tail of its large deviations). The results also transfer to the left tail…
Turbulence exhibits significant velocity fluctuations even if the scale is much larger than the scale of the energy supply. Since any spatial correlation is negligible, these large-scale fluctuations have many degrees of freedom and are…
The fluctuations in nonequilibrium systems are under intense theoretical and experimental investigation. Topical ``fluctuation relations'' describe symmetries of the statistical properties of certain observables, in a variety of models and…
Extensive time-series encoding the position of particles such as viruses, vesicles, or individual proteins are routinely garnered in single-particle tracking experiments or supercomputing studies. They contain vital clues on how viruses…
Stochasticity can play an important role in the dynamics of biologically relevant populations. These span a broad range of scales: from intra-cellular populations of molecules to population of cells and then to groups of plants, animals and…
We consider different models of stochastic dissipative equations and theoretically compute the probability distribution functions (actually the associated large deviation functions) of the time averaged injected power required to sustain a…
We present and establish large deviations principles for general multivariate renewal-reward processes associated with a classical discrete-time renewal process. A renewal-reward process describes a cumulative reward over time, supposing…
The work relates to a new way for analysis of one-dimensional stochastic systems, based on consideration of its higher order difference structure. From this point of view, the deterministic and random processes are analyzed. A new numerical…
We study the large fluctuations of emitted radiations in the system of $N$ non-interacting two-level atoms. Two methods are used to calculate the probability of the large fluctuations and the time dependence of the excitation and emission.…