Related papers: Truncated linear statistics in the one dimensional…
We study the fluctuations of the largest eigenvalue $\lambda_{\max}$ of $N \times N$ random matrices in the limit of large $N$. The main focus is on Gaussian $\beta$-ensembles, including in particular the Gaussian orthogonal ($\beta=1$),…
The present Letter, deals with the statistical theory [Phys. Rev. E {\bf 66}, 056125 (2002) and Phys. Rev E {\bf 72}, 036108 (2005)], which predicts the probability distribution $p(E) \propto \exp_{\kappa} (-I)$, where, $I \propto \beta E…
An invariant ensemble of $N\times N$ random matrices can be characterised by a joint distribution for eigenvalues $P(\lambda_1,\cdots,\lambda_N)$. The study of the distribution of linear statistics, i.e. of quantities of the form…
Particle density fluctuations in the scrape-off layer of magnetically confined plasmas, as measured by gas-puff imaging or Langmuir probes, are modeled as the realization of a stochastic process in which a superposition of pulses with a…
We investigate the work fluctuations in an overdamped non-equilibrium process that is stopped at a stochastic time. The latter is characterized by a first passage event that marks the completion of the non-equilibrium process. In…
A truncated partial-wave analysis is performed for $\eta$-photoproduction using the polarization observables $\sigma_0, \Sigma, T, E, F$ and $G$. Different truncation orders are analyzed for six energy bins within the range of…
Bursty transport phenomena associated with convective motion present universal statistical characteristics among different physical systems. In this letter, a stochastic univariate model and the associated probability distribution function…
From the perspective of non-equilibrium statistical mechanics, modeling the velocity distribution of particles in non-equilibrium, steady-state plasmas presents a significant challenge. Under this context, a family of kappa distributions…
We develop a stochastic model for the charge fluctuations on a microscopic dust particle resting on a surface exposed to plasma. We find in steady state that the fluctuations are normally distributed with a standard deviation that is…
This paper is the continuation of a previous one [L. {\v{S}}amaj and B. Jancovici, 2007 {\it J. Stat. Mech.} P02002]; for a nearly classical quantum fluid in a half-space bounded by a plain plane hard wall (no image forces), we had…
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…
For the two-dimensional one-component Coulomb plasma, we derive an asymptotic expansion of the free energy up to order $N$, the number of particles of the gas, with an effective error bound $N^{1-\kappa}$ for some constant $\kappa > 0$.…
The equation of state with quantum statistics corrections is used for particle number fluctuations $\omega$ of isotopically symmetric nuclear matter with interparticle van der Waals and Skyrme local density interactions. The fluctuations,…
We consider the classical Coulomb gas in two dimensions at the inverse temperature $\beta=2$, confined within a droplet of radius $R$ by a rotationally invariant potential $U(r)$. For $U(r)\sim r^2$ this describes the eigenvalues of the…
We study the full distribution $P_{N}\left(A\right)$ of sums $A = \sum_{i=1}^N$ where $x_1, \dots, x_N$ are $N \gg 1$ independent and identically distributed random variables each sampled from a given distribution $p(x)$ with a…
We consider a one-dimensional symmetric simple exclusion process in contact with slowed reservoirs: at the left (resp. right) boundary, particles are either created or removed at rates given by $\alpha/n$ or $(1-\alpha)/n$ (resp. $\beta/n$…
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…
This work extends Favard-type spectral representations for banded matrices $T$ beyond the bounded setting. It assumes that, for every $N\in\mathbb N_0$, there exists a shift $s_N\ge 0$ such that the shifted truncation $A_N:= T^{[N]}+s_N…
We study the dynamics of a one-dimensional run and tumble particle subjected to confining potentials of the type $V(x) = \alpha \, |x|^p$, with $p>0$. The noise that drives the particle dynamics is telegraphic and alternates between $\pm 1$…
The dispersion relation of longitudinal electrostatic oscillations in a relativistic plasma is studied in the context of the nonextensive statistics formalism proposed by Tsallis [C. Tsallis, J. Stat. Phys. {\bf 52}, 479 (1988)], where…