Related papers: Extreme value statistics in coupled lasers
A new method to simulate probability distributions in regions where the events are VERY unlikely (e.g. p ~ 10^{-40}) is presented. The basic idea is to represent the underlying probability space by the phase space of a physical system. The…
We investigate some implications of the freezing scenario proposed by Carpentier and Le Doussal (CLD) for a random energy model (REM) with logarithmically correlated random potential. We introduce a particular (circular) variant of the…
In this paper, we investigate the crossing statistics of speckle patterns formed in Fresnel diffraction region by a laser beam scattering through a nanofluid. We extend $zero-crossing$ statistics to assess dynamical properties of nanofluid.…
It has been shown that sufficiently well mixing dynamical systems with positive entropy have extreme value laws which in the limit converge to one of the three standard distributions known for i.i.d. processes, namely Gumbel, Fr\'echet and…
A stochastic model is presented for a super-position of uncorrelated pulses with a random distribution of amplitudes, sizes, velocities and arrival times. The pulses are assumed to move radially with fixed shape and amplitudes decaying…
We investigate the extreme value statistics connected with the dilute Random Energy Model with integer couplings. New universality class is found.
We study the two-species diffusion-annihilation process, $A+B\rightarrow$ \O, on the fully-connected lattice. Probability distributions for the number of particles and the reaction time are obtained for a finite-size system using a master…
In this paper, we view fluctuating fronts made of particles on a one-dimensional lattice as an extreme value problem. The idea is to denote the configuration for a single front realization at time $t$ by the set of co-ordinates…
Let $(X_i)_{1 \le i \le n}$ be independent and identically distributed (i.i.d.) standard Gaussian random variables, and denote by $X_{(n)} = \max_{1 \le i \le n} X_i$ the maximum order statistic. It is well-known in extreme value theory…
A pedagogical account of some aspects of Extreme Value Statistics (EVS) is presented from the somewhat non-standard viewpoint of Large Deviation Theory. We address the following problem: given a set of $N$ i.i.d. random variables…
While averages and typical fluctuations often play a major role to understand the behavior of a non-equilibrium system, this nonetheless is not always true. Rare events and large fluctuations are also pivotal when a thorough analysis of the…
We consider maximum likelihood estimation with data from a bivariate Gaussian process with a separable exponential covariance model under fixed domain asymptotic. We first characterize the equivalence of Gaussian measures under this model.…
In this paper, we consider projection estimates for L\'evy densities in high-frequency setup. We give a unified treatment for different sets of basis functions and focus on the asymptotic properties of the maximal deviation distribution for…
Anomalous diffusion and non-Gaussian statistics are detected experimentally in a two-dimensional driven-dissipative system. A single-layer dusty plasma suspension with a Yukawa interaction and frictional dissipation is heated with laser…
Broad-area semiconductor lasers are employed in many high-power applications, however, their spatio-temporal dynamics is complex and intrinsically unstable due to the interaction of several transverse lasing modes. A dynamical and…
Maximum-type statistics of certain functions of the sample covariance matrix of high-dimensional vector time series are studied to statistically confirm or reject the null hypothesis that a data set has been collected under normal…
We study analytically and numerically the extreme value distribution of observables defined along the temporal evolution of a dynamical system. The convergence to the Gumbel law of observable recurrences gives information on the fractal…
For a skew normal random sequence, convergence rates of the distribution of its partial maximum to the Gumbel extreme value distribution are derived. The asymptotic expansion of the distribution of the normalized maximum is given under an…
The generalized extreme value distribution and its particular case, the Gumbel extreme value distribution, are widely applied for extreme value analysis. The Gumbel distribution has certain drawbacks because it is a non-heavy-tailed…
Extreme value functionals of stochastic processes are inverse functionals of the first passage time -- a connection that renders their probability distribution functions equivalent. Here, we deepen this link and establish a framework for…