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Large deviation principles and complete equivalence and nonequivalence results for pure and mixed ensembles
Statistics turbulent coherent structures mechanical model the model of two-dimensional fluid motion
2014/12/29
We consider a general class of statistical mechanical models of coherent structures in turbulence, which includes models of two-dimensional fluid motion, quasi-geostrophic flows, and dispersive waves....
Nonequivalent statistical equilibrium ensembles and refined stability theorems for most probable flows
Two-dimensional correlation structure of equilibrium model the model of energy balance ratio model water resources
2014/12/29
Statistical equilibrium models of coherent structures in two-dimensional and barotropic quasi-geostrophic turbulence are formulated using canonical and microcanonical ensembles, and the equivalence or...
An introduction to the thermodynamic and macrostate levels of nonequivalent ensembles
The contour the thermodynamics macro status the equivalent amount of collection
2014/12/29
This short paper presents a nontechnical introduction to the problem of nonequivalent microcanonical and canonical ensembles. Both the thermodynamic and the macrostate levels of definition of nonequiv...
Thermodynamic versus statistical nonequivalence of ensembles for the mean-field Blume-Emery-Griffiths model
Not equivalent statistical mechanics testing model not equivalent common thermodynamics
2014/12/29
We illustrate a novel characterization of nonequivalent statistical mechanical ensembles using the mean-field Blume–Emery–Griffiths (BEG) model as a test model. The novel characterization takes effect...
Generalized canonical ensembles and ensemble equivalence
Boltzmann continuous function generalized canonical ensemble and physics
2014/12/25
This paper is a companion piece to our previous work [J. Stat. Phys. 119, 1283 (2005)], which introduced a generalized canonical ensemble obtained by multiplying the usual Boltzmann weight factor e...
Nonconcave entropies from generalized canonical ensembles
Microcanonical ensemble entropy the curies - Weiss - Potts spin model model
2014/12/25
It is well known that the entropy of the microcanonical ensemble cannot be calculated as the Legendre transform of the canonical free energy when the entropy is nonconcave. To circumvent this problem,...
Best-fit quasi-equilibrium ensembles: a general approach to statistical closure of underresolved Hamiltonian dynamics
Reduce model Hamiltonian dynamics system model reduction space
2014/12/24
A new method of deriving reduced models of Hamiltonian dynamical systems is developed using techniques from optimization and statistical estimation. Given a set of resolved variables that define a mod...
MCMC for non-linear state space models using ensembles of latent sequences
MCMC non-linear state space models ensembles latent sequences
2013/6/13
Non-linear state space models are a widely-used class of models for biological, economic, and physical processes. Fitting these models to observed data is a difficult inference problem that has no str...
Classification Loss Function for Parameter Ensembles in Bayesian Hierarchical Models
Classification Loss Function Parameter Ensembles Bayesian Hierarchical Models
2011/6/20
Our perspective in this paper follows the framework adopted by Lin et al. (2006), who intro-
duced several loss functions for the identi cation of the elements of a parameter ensemble that
represent...
Asymptotic behavior of random determinants in the Laguerre, Gram and Jacobi ensembles
Random matrices Wishart ensemble Laguerre ensemble Jacobi ensemble Gram ensemble Hadamard ratio determinant invariance principle large deviations
2009/6/12
Asymptotic behavior of random determinants in the Laguerre, Gram and Jacobi ensembles.
Orthogonal polynomial ensembles in probability theory
Random matrix theory Vandermonde determinant GUE orthogonal polynomial method bulk and edge scaling
2009/5/18
We survey a number of models from physics, statistical mechanics, probability theory and combinatorics, which are each described in terms of an {it orthogonal polynomial ensemble}. The most prominent ...
Wigner theorems for random matrices with dependent entries：Ensembles associated to symmetric spaces and sample covariance matrices
Wigner theorem symmetric space sample covariance
2009/3/20
It is a classical result of Wigner that for an hermitian matrix with independent entries on and above the diagonal, the mean empirical eigenvalue distribution converges weakly to the semicircle law as...
Universality results for largest eigenvalues of some sample covariance matrix ensembles
Universality results largest eigenvalues sample covariance matrix ensembles
2010/4/29
For sample covariance matrices with iid entries with sub-Gaussian
tails, when both the number of samples and the number of variables
become large and the ratio approaches to one, it is a well-known ...