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The Generalized Central Limit Theorem is a remarkable generalization of the Central Limit Theorem, showing that the sum of a large number of independent, identically-distributed (i.i.d) random variables with infinite variance may converge…
We consider fluctuations of the dissipated energy in nonlinear driven diffusive systems subject to bulk dissipation and boundary driving. With this aim, we extend the recently-introduced macroscopic fluctuation theory to nonlinear driven…
We propose a revised definition of quasi-distributions within the framework of large-momentum effective theory (LaMET) that improves convergence towards the large-momentum limit. Since the definition of quasi-distributions is not unique,…
In the context of the mixing dynamical systems we present a derivation of the Gaussian ensembles distributions from mixing quantum systems having a classical analog that is mixing. We find that mixing factorization property is satisfied for…
The sub-Gaussian stable distribution is a heavy-tailed elliptically contoured law which has interesting applications in signal processing and financial mathematics. This work addresses the problem of feasible estimation of distributions. We…
The equations of motion for the density modes of a fluid, derived from Newton's equations, are written as a linear generalized Langevin equation. The constraint imposed by the fluctuation-dissipation theorem is used to derive an exact form…
We propose flexible Gaussian representations for conditional cumulative distribution functions and give a concave likelihood criterion for their estimation. Optimal representations satisfy the monotonicity property of conditional cumulative…
Under certain conditions on k we calculate the limit distribution of the k:th largest eigenvalue, x_k, of the Gaussian Unitary Ensemble (GUE). More specifically, if n is the dimension of a random matrix from the GUE and k is such that both…
Many complex systems are characterized by non-Boltzmann distribution functions of their statistical variables. If one wants to -- justified or not -- hold on to the maximum entropy principle for complex statistical systems (non-Boltzmann)…
We consider a many particle quantum system, in which each particle interacts only with its nearest neighbours. Provided that the energy per particle has an upper bound, we show, that the energy distribution of almost every product state…
We study distributions of random vectors whose components are second order polynomials in Gaussian random variables. Assuming that the law of such a vector is not absolutely continuous with respect to Lebesgue measure, we derive some…
Gaussian comparison inequalities provide a way of bounding probabilities relating to multivariate Gaussian random vectors in terms of probabilities of random variables with simpler correlation structures. In this paper, we establish the…
A Gaussian fluctuation formula is proved for linear statistics of complex random matrices in the case that the statistic is rotationally invariant. For a general linear statistic without this symmetry, Coulomb gas theory is used to predict…
The dynamics of a one-dimensional stochastic model is studied in presence of an absorbing boundary. The distribution of fluctuations is analytically characterized within the generalized van Kampen expansion, accounting for higher order…
We start by reviewing recent probabilistic results on ergodic sums in a large class of (non-uniformly) hyperbolic dynamical systems. Namely, we describe the central limit theorem, the almost-sure convergence to the gaussian and other stable…
In this article we review recent generalisations of the central limit theorem for the sum of specially correlated (or q-independent) variables, focusing on q greater or equal than 1. Specifically, this kind of correlation turns the…
The purpose of this note is to show how simple Optimal Transport arguments, on the real line, can be used in Superconcentration theory. This methodology is efficient to produce sharp non-asymptotic variance bounds for various functionals…
Symmetries play a conspicuous role in the large-scale behavior of critical systems. While in equilibrium they allow to classify asymptotics into different universality classes, out of equilibrium they can emerge, some times unexpectedly, as…
A mechanism is proposed for the appearance of power law distributions in various complex systems. It is shown that in a conservative mechanical system composed of subsystems with different numbers of degrees of freedom a robust power-law…
Starting from the most general formulation of stochastic thermodynamics---i.e. a thermodynamically consistent nonautonomous stochastic dynamics describing systems in contact with several reservoirs---, we define a procedure to identify the…