Related papers: Extreme value statistics in coupled lasers
Count data are omnipresent in many applied fields, often with overdispersion due to an excess of zeroes or extreme values. With mixtures of Poisson distributions representing an elegant and appealing modelling strategy, we focus here on the…
Flexible random scale-mixture models provide a framework for capturing a broad range of extremal dependence structures. However, likelihood-based inference under the peaks-over-threshold setting is often computationally infeasible, due to…
In this note, we establish the convergence in distribution of the maxima of i.i.d. random variables to the Gumbel distribution with the associated normalizing sequences for several examples that are related to the normal distribution.…
We study the statistics and scaling of extreme fluctuations in noisy task-completion landscapes, such as those emerging in synchronized distributed-computing networks, or generic causally-constrained queuing networks, with scale-free…
Gibbsian statistical mechanics is extended into the domain of non-negligible {though non-specified} correlations in phase space while respecting the fundamental laws of thermodynamics. The appropriate Gibbsian probability distribution is…
We study analytically the distribution of the minimum of a set of hierarchically correlated random variables $E_1$, $E_2$, $...$, $E_N$ where $E_i$ represents the energy of the $i$-th path of a directed polymer on a Cayley tree. If the…
Let $\{X_i(t),t\ge0\}, 1\le i\le n$ be independent copies of a stationary process $\{X(t), t\ge0\}$. For given positive constants $u,T$, define the set of $r$th conjunctions $ C_{r,T,u}:= \{t\in [0,T]: X_{r:n}(t) > u\}$ with $X_{r:n}(t)$…
Gibbs-type exchangeable random partitions, which is a class of multiplicative measures on the set of positive integer partitions, appear in various contexts, including Bayesian statistics, random combinatorial structures, and stochastic…
The peculiar characteristics of random laser emission have been studied in many different media, leading to a classification of the working regimes based on the statistics of spectral fluctuations. Alongside such studies, the possibility to…
Assessing the significance of alignment scores of optimally aligned DNA or amino acid sequences can be achieved via the knowledge of the score distribution of random sequences. But this requires obtaining the distribution in the…
We investigate the rate of convergence toward the Boolean extreme value distribution, which is the universal limiting law for the normalized spectral maximum of Boolean independent and identically distributed positive operators, under the…
Efficient simulation of the timing jitter in passively mode-locking lasers is key to their numerical investigation and optimization. We introduce a method based on the pulse-period fluctuation auto-correlation function and compare it…
We compute the full order statistics of a one-dimensional gas of fermions in a harmonic trap at zero temperature, including its large deviation tails. The problem amounts to computing the probability distribution of the $k$th smallest…
Graphical models are commonly used tools for modeling multivariate random variables. While there exist many convenient multivariate distributions such as Gaussian distribution for continuous data, mixed data with the presence of discrete…
We study statistical properties of the energy spectra of two-dimensional quasiperiodic tight-binding models. The multifractal nature of the eigenstates of these models is corroborated by the scaling of the participation numbers with the…
We consider the statistics of volume fluctuations in a one-dimensional classical gas of non-interacting particles confined by a piston, and subjected to an arbitrary external potential. We show that despite the absence of interactions…
An experimental study of the delayed threshold phenomenon in a Vertical Extended Cavity Semiconductor Emitting Laser is carried out. Under modulation of the pump power, the laser intensity exhibits a hysteresis behavior in the vicinity of…
Since the analogy between laser oscillation and second-order phase transition was indicated in the 1970s, dynamical fluctuations on lasing threshold inherent in critical phenomena have gained significant interest. Here, we numerically and…
A stochastic model for a superposition of uncorrelated pulses with a random distribution of amplitudes, sizes, and velocities is analyzed. The pulses are assumed to move radially with fixed shape and amplitudes decreasing exponentially in…
In this paper we perform an analytical and numerical study of Extreme Value distributions in discrete dynamical systems that have a singular measure. Using the block maxima approach described in Faranda et al. [2011] we show that,…