Related papers: Extreme value statistics in coupled lasers
In this thesis, we study three physically relevant models of strongly correlated random variables: trapped fermions, random matrices and random walks. In the first part, we show several exact mappings between the ground state of a trapped…
We derive a general expression that quantifies the total entanglement production rate in continuous variable systems, where a source emits two entangled Gaussian beams with arbitrary correlators.This expression is especially useful for…
In the paper a model of a single-atom laser with incoherent pumping is theoretically investigated. In the stationary case, a linear homogeneous differential equation for the phase-averaged Hussimi Q-function is derived from the equation for…
This work proposes a scalable probabilistic latent variable model based on Gaussian processes (Lawrence, 2004) in the context of multiple observation spaces. We focus on an application in astrophysics where data sets typically contain both…
We characterize the operation of semiconductor microring lasers in an excitable regime. Our experiments reveal a statistical distribution of the characteristics of noise-triggered optical pulses that is not observed in other excitable…
The low temperature physics of disordered systems is governed by the statistics of extremely low energy states. It is thus rather important to discuss the possible universality classes for extreme value statistics. We compare the usual…
This work focuses on the incoherent and coherent combination of pulsed laser beams, building on previous research [1] that addressed the combination of continuous-wave laser beams. For the pulsed combination, we have focused on the temporal…
A laser exhibits both controllable gain and loss and, under proper design conditions, is an ideal non-Hermitian system allowing the direct observation and engineering of spectral singularities such as exceptional points (EPs). A dual…
We study the problem of estimating the covariance parameters of a one-dimensional Gaussian process with exponential covariance function under fixed-domain asymptotics. We show that the weighted pairwise maximum likelihood estimator of the…
Gaussian mixture models are central to classical statistics, widely used in the information sciences, and have a rich mathematical structure. We examine their maximum likelihood estimates through the lens of algebraic statistics. The MLE is…
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…
Complex systems performing spiking dynamics are widespread in Nature. They cover from earthquakes, to neurons, variable stars, social networks, or stock markets. Understanding and characterizing their dynamics is relevant in order to detect…
Detailed experimental and theoretical investigations on two coupled fiber lasers, each with many longitudinal modes, reveal that the behavior of the longitudinal modes depends on both the coupling strength as well as the detuning between…
The dynamics of a laser-excited Rydberg electron under the influence of a fluctuating laser field are investigated. Rate equations are developed which describe these dynamics in the limit of large laser bandwidths for arbitrary types of…
We investigate extreme value theory for physical systems with a global conservation law which describe renewal processes, mass transport models and long-range interacting spin models. As shown previously, a special feature is that the…
We studied the statistical properties of a quantum system in the pseudo-integrable regime through the gap ratios between consecutive energy levels of the scattering spectra. A two-dimensional quantum billiard containing a point-like…
The statistical properties of three-level lasing are investigated theoretically. It is assumed that the three-level medium is coherently excited by another laser with an arbitrary photon statistics. It is proved that, under the specific…
It is well-known that the expected scaled maximum of non-negative random variables with unit mean defines a stable tail dependence function associated with some extreme-value copula. In the special case when these random variables are…
The work presents a proof of convergence of the density of energy levels to a Gaussian distribution for a wide class of quadratic forms of Fermi operators. This general result applies also to quadratic operators with disorder, e.g.,…
We show that the probability of appearance of synchronisation in chaotic coupled map lattices is related to the distribution of the maximum of a certain observable evaluated along almost all orbit. We show that such distribution belongs to…