Related papers: Large deviations, condensation, and giant response…
A generalization of a distribution increases the flexibility particularly in studying of a phenomenon and its properties. Many generalizations of continuous univariate distributions are available in literature. In this study, an…
Fluctuations in the statistical model of heavy ion collisions are studied. The role of statistics, relativity, constraints, decaying resonances and branching processes are investigated using this model. Also studied are thermodynamic…
A finite dimensional quantum system for which the quantum chaos conjecture applies has eigenstates, which show the same statistical properties than the column vectors of random orthogonal or unitary matrices. Here, we consider the different…
We apply the scale-length method to several three dimensional samples of the Two degree Field Galaxy Redshift Survey. This method allows us to map in a quantitative and powerful way large scale structures in the distribution of galaxies…
Thermodynamic stability of statistical systems requires that susceptibilities be semipositive and finite. Susceptibilities are known to be related to the fluctuations of extensive observable quantities. This relation becomes nontrivial,…
We study the phenomenon of real space condensation in the steady state of a class of mass transport models where the steady state factorises. The grand canonical ensemble may be used to derive the criterion for the occurrence of a…
The fluctuation-dissipation theorem is a central result in statistical mechanics and is usually formulated for systems described by diffusion processes. In this paper, we propose a generalization for a wider class of stochastic processes,…
Large random matrices appear in different fields of mathematics and physics such as combinatorics, probability theory, statistics, operator theory, number theory, quantum field theory, string theory etc... In the last ten years, they…
We study the universal nature of global fluctuations in the critical regime of the spherical model by evaluating the exact distribution of the magnetization and its absolute value in the thermodynamical limit, in the presence of a conjugate…
Large deviation results are given for a class of perturbed nonhomogeneous Markov chains on finite state space which formally includes some stochastic optimization algorithms. Specifically, let {P_n} be a sequence of transition matrices on a…
The fluctuation-dissipation theorem is a cornerstone result in statistical mechanics that can be used to translate the statistics of the free natural variability of a system into information on its forced response to perturbations. By…
We obtain the exact large deviation functions of the density profile and of the current, in the non-equilibrium steady state of a one dimensional symmetric simple exclusion process coupled to boundary reservoirs with slow rates. Compared to…
The organization of high-dimensional probability spaces is a fundamental problem at the intersection of statistical physics and information theory. Here, we analyze the distributions populating level surfaces of the probability simplex…
Stationary non-equilibrium states describe steady flows through macroscopic systems. Although they represent the simplest generalization of equilibrium states, they exhibit a variety of new phenomena. Within a statistical mechanics…
How condensed-matter simulations depend on the number of molecules being simulated ($N$) is sometimes itself a valuable piece of information. Liquid crystals provide a case in point. Light scattering and $2d$-IR experiments on…
Earlier we showed that the fine structure of the spectrum of amplitude variations in the results of measurements of the processes of different nature (in other words, the fine structure of the dispersion of results or the pattern of the…
We study a large deviation functional of density fluctuation by analyzing stochastic non-linear diffusion equations driven by the difference between the densities fixed at the boundaries. By using a fundamental equality that yields the…
We present a thermodynamic theory for a generic population of $M$ individuals distributed into $N$ groups (clusters). We construct the ensemble of all distributions with fixed $M$ and $N$, introduce a selection functional that embodies the…
The statistical mechanical basis of the fluctuation theory of mixtures is reviewed. An overview of the statistical mechanical relations between the microscopic properties of a system and its macroscopic properties is presented. The…
These lecture notes give a short review of methods such as the matrix ansatz, the additivity principle or the macroscopic fluctuation theory, developed recently in the theory of non-equilibrium phenomena. They show how these methods allow…