Related papers: Extreme value statistics in coupled lasers
In ultra-fast multi-mode lasers, mode-locking is implemented by means of ad hoc devices, like saturable absorbers or modulators, allowing for very short pulses. This comes about because of nonlinear interactions induced among modes at…
An exact analytical description of extreme intensity statistics in complex random states is derived. These states have the statistical properties of the Gaussian and Circular Unitary Ensemble eigenstates of random matrix theory. Although…
This paper will deal with isolated laser pulses, those which last for a finite time interval and whose envelope function is strictly zero outside of this interval. We numerically calculate the Fourier transform of this function and study…
We propose a new approach, based on statistical mechanics, to predict the saturated state of a single-pass, high-gain free-electron laser (FEL). In analogy with the violent relaxation process in self-gravitating systems and in the Euler…
A discrete version of the Gumbel (Type I) extreme value distribution has been derived by using the general approach of discretization of a continuous distribution. Important distributional and reliability properties have been explored. It…
Gain-switched lasers are in demand in numerous quantum applications, particularly, in systems of quantum key distribution and in various optical quantum random number generators. The reason for this popularity is natural phase randomization…
We show how two electrically coupled semiconductor lasers having optical feedback can present simultaneous anti-phase correlated fast power fluctuations, and strong in-phase synchronized spikes of chaotic power drops. This quite counter…
Extreme value statistics, or extreme statistics for short, refers to the statistics that characterizes rare events of either unusually high or low intensity: climate disasters like floods following extremely intense rains are among the…
In the framework of Cramer's probabilistic model of primes, we explore the exact and asymptotic distributions of maximal prime gaps. We show that the Gumbel extreme value distribution exp(-exp(-x)) is the limit law for maximal gaps between…
Extreme values are considered in samples with random size that has a mixed Poisson distribution being generated by a doubly stochastic Poisson process. We prove some inequalities providing bounds on the rate of convergence in limit theorems…
Extreme events (sometimes also called optical rogue waves), in the form of pulses of extraordinary intensity, are easily observed in its chaotic regime if the Fresnel number of the cavity is high. This result suggests that the nonlinear…
Seemingly unrelated linear regression models are introduced in which the distribution of the errors is a finite mixture of Gaussian components. Identifiability conditions are provided. The score vector and the Hessian matrix are derived.…
Almost all scientific data have uncertainties originating from different sources. Gaussian process regression (GPR) models are a natural way to model data with Gaussian-distributed uncertainties. GPR also has the benefit of reducing I/O…
We report a new configuration and theoretical approach for the study of the incoherent and coherent combination of Gaussian laser beams which allows us to calculate the combined intensity at every point in space, this new approach consists…
We propose a new class of extreme-value copulas which are extreme-value limits of conditional normal models. Conditional normal models are generalizations of conditional independence models, where the dependence among observed variables is…
Modern data sets in various domains often include units that were sampled non-randomly from the population and have a latent correlation structure. Here we investigate a common form of this setting, where every unit is associated with a…
Building upon the one-step replica symmetry breaking formalism, duly understood and ramified, we show that the sequence of ordered extreme values of a general class of Euclidean-space logarithmically correlated random energy models…
We quantify the large deviations of Gaussian extreme value statistics on closed convex sets in d-dimensional Euclidean space. The asymptotics imply that the extreme value distribution exhibits a rate function that is a simple quadratic…
Representing an ensemble of random lasers with an ensemble of random matrices, we compute average number of lasing modes and its fluctuations. The regimes of weak and strong coupling of the passive resonator to environment are considered.…
Controlled experimental studies of percolation are challenging due to difficulties in tuning site connectivity, isolating local interactions, and mitigating finite-size effects. In this work, we experimentally investigate percolation with a…