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Related papers: Fluctuation formula for complex random matrices

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We prove Gaussian fluctuation for pair counting statistics of the form $ \sum_{1\leq i\neq j\leq N} f(\theta_i-\theta_j)$ for the Circular Unitary Ensemble (CUE) of random matrices in the case of a slowly growing variance in the limit of…

Probability · Mathematics 2021-02-03 Ander Aguirre , Alexander Soshnikov

We study the dynamics of the fluctuations of the variance $s$ of the order parameter of the Gaussian model, following a temperature quench of the thermal bath. At each time $t$, there is a critical value $s_c(t)$ of $s$ such that…

Statistical Mechanics · Physics 2020-09-11 Federico Corberi , Onofrio Mazzarisi , Andrea Gambassi

Fluctuation theorems have a very special place in the study of non equilibrium dynamics of physical systems. The form in which it is used most extensively is the Gallavoti-Cohen Fluctuation Theorem which is in terms of the distribution of…

Classical Physics · Physics 2015-12-01 G. S. Agarwal , Sushanta Dattagupta

We prove a central limit theorem for the difference of linear eigenvalue statistics of a sample covariance matrix $\widetilde{W}$ and its minor $W$. We find that the fluctuation of this difference is much smaller than those of the…

Probability · Mathematics 2021-11-23 Giorgio Cipolloni , László Erdős

The discrete Boltzmann equation for both the ideal and a non-ideal fluid is extended by adding Langevin noise terms in order to incorporate the effects of thermal fluctuations. After casting the fluctuating discrete Boltzmann equation in a…

Computational Physics · Physics 2011-04-01 M. Gross , M. E. Cates , F. Varnik , R. Adhikari

We employ the macroscopic fluctuation theory to study fluctuations of integrated current in one-dimensional lattice gases with a step-like initial density profile. We analytically determine the variance of the current fluctuations for a…

Statistical Mechanics · Physics 2015-06-05 P. L. Krapivsky , Baruch Meerson

The Macroscopic Fluctuation Theory is an effective framework to describe transports and their fluctuations in classical out-of-equilibrium diffusive systems. Whether the Macroscopic Fluctuation Theory may be extended to the quantum realm…

Statistical Mechanics · Physics 2021-11-05 Denis Bernard

In the last decade, spectral linear statistics on large dimensional random matrices have attracted significant attention. Within the physics community, a privileged role has been played by invariant matrix ensembles for which a two…

Mathematical Physics · Physics 2016-02-18 Fabio Deelan Cunden , Paolo Facchi , Pierpaolo Vivo

We present a generalized integral fluctuation theorem (GIFT) for general diffusion processes using the Feynman-Kac and Cameron-Martin-Girsanov formulas. Existing IFTs can be thought of to be its specific cases. We interpret the origin of…

Statistical Mechanics · Physics 2015-05-13 Fei Liu , Zhong-can Ou-Yang

Understanding the physics of non-equilibrium systems remains as one of the major open questions in statistical physics. This problem can be partially handled by investigating macroscopic fluctuations of key magnitudes that characterise the…

Soft Condensed Matter · Physics 2016-11-17 A. Lasanta , Pablo I. Hurtado , A. Prados

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…

Econometrics · Economics 2025-04-22 Richard Spady , Sami Stouli

A thermodynamic-like formalism is developed for superstatistical systems based on conditional entropies. This theory takes into account large-scale variations of intensive variables of systems in nonequilibrium stationary states. Ordinary…

Statistical Mechanics · Physics 2009-11-13 Sumiyoshi Abe , Christian Beck , E. G. D. Cohen

We consider nonequilibrium systems with complex dynamics in stationary states with large fluctuations of intensive quantities (e.g. the temperature, chemical potential, or energy dissipation) on long time scales. Depending on the…

Statistical Mechanics · Physics 2009-11-07 C. Beck , E. G. D. Cohen

This paper is devoted to the Gaussian fluctuations and deviations of the traces of tridiagonal random matrix. Under quite general assumptions, we prove that the traces are approximately normal distributed. Multi-dimensional central limit…

Probability · Mathematics 2015-06-16 Deng Zhang

Cosmological perturbations due to statistical thermal fluctuations in a single fluid characterized by an arbitrary equation of state are computed. Formulas to predict the scalar and tensor perturbation spectra and nongaussianity parameters…

Cosmology and Nongalactic Astrophysics · Physics 2013-08-09 Tirthabir Biswas , Robert Brandenberger , Tomi Koivisto , Anupam Mazumdar

The fluctuation theorem is a pivotal result of statistical physics. It quantifies the probability of observing fluctuations which are in violation of the second law of thermodynamics. More specifically, it quantifies the ratio of the…

Statistical Mechanics · Physics 2011-08-26 M. Belushkin , R. Livi , G. Foffi

In this note we want to have another look on Schwinger-Dyson equations for the eigenvalue distributions and the fluctuations of classical unitarily invariant random matrix models. We are exclusively dealing with one-matrix models, for which…

Operator Algebras · Mathematics 2013-07-09 James A. Mingo , Roland Speicher

The estimation of mutation probabilities and relative fitnesses in fluctuation analysis is based on the unrealistic hypothesis that the single-cell times to division are exponentially distributed. Using the classical Luria-Delbr\"{u}ck…

Quantitative Methods · Quantitative Biology 2014-03-05 Bernard Ycart

Fluctuation theorems make use of time reversal to make predictions about entropy production in many-body systems far from thermal equilibrium. Here we review the wide variety of distinct, but interconnected, relations that have been derived…

Statistical Mechanics · Physics 2007-08-02 R. J. Harris , G. M. Schütz

We suggest an extension of the standard concept of statistical ensembles. Namely, we introduce a class of ensembles with extensive quantities fluctuating according to an externally given distribution. As an example the influence of energy…

Nuclear Theory · Physics 2008-11-26 M. I. Gorenstein , M. Hauer