114,254 research outputs found
Entropy Coherent and Entropy Convex Measures of Risk
We introduce two subclasses of convex measures of risk, referred to as entropy coherent and entropy convex measures of risk. We prove that convex, entropy convex and entropy coherent measures of risk emerge as certainty equivalents under variational, homothetic and multiple priors preferences, respectively, upon requiring the certainty equivalents to be translation invariant. In addition, we study the properties of entropy coherent and entropy convex measures of risk, derive their dual conjugate function, and prove their distribution invariant representation. Some financial applications and examples of entropy coherent and entropy convex measures of risk are also investigated.Multiple priors;Variational and homothetic preferences;Robustness;Convex risk measures;Exponential utility;Relative entropy;Translation invariance;Convexity;Indifference valuation
Weakly Nonextensive Thermostatistics and the Ising Model with Long--range Interactions
We introduce a nonextensive entropic measure that grows like
, where is the size of the system under consideration. This kind
of nonextensivity arises in a natural way in some -body systems endowed with
long-range interactions described by interparticle potentials.
The power law (weakly nonextensive) behavior exhibited by is
intermediate between (1) the linear (extensive) regime characterizing the
standard Boltzmann-Gibbs entropy and the (2) the exponential law (strongly
nonextensive) behavior associated with the Tsallis generalized -entropies.
The functional is parametrized by the real number
in such a way that the standard logarithmic entropy is recovered when
>. We study the mathematical properties of the new entropy, showing that the
basic requirements for a well behaved entropy functional are verified, i.e.,
possesses the usual properties of positivity, equiprobability,
concavity and irreversibility and verifies Khinchin axioms except the one
related to additivity since is nonextensive. For , the
entropy becomes superadditive in the thermodynamic limit. The
present formalism is illustrated by a numerical study of the thermodynamic
scaling laws of a ferromagnetic Ising model with long-range interactions.Comment: LaTeX file, 20 pages, 7 figure
Exponential Decay of Correlations Implies Area Law
We prove that a finite correlation length, i.e. exponential decay of
correlations, implies an area law for the entanglement entropy of quantum
states defined on a line. The entropy bound is exponential in the correlation
length of the state, thus reproducing as a particular case Hastings proof of an
area law for groundstates of 1D gapped Hamiltonians.
As a consequence, we show that 1D quantum states with exponential decay of
correlations have an efficient classical approximate description as a matrix
product state of polynomial bond dimension, thus giving an equivalence between
injective matrix product states and states with a finite correlation length.
The result can be seen as a rigorous justification, in one dimension, of the
intuition that states with exponential decay of correlations, usually
associated with non-critical phases of matter, are simple to describe. It also
has implications for quantum computing: It shows that unless a pure state
quantum computation involves states with long-range correlations, decaying at
most algebraically with the distance, it can be efficiently simulated
classically.
The proof relies on several previous tools from quantum information theory -
including entanglement distillation protocols achieving the hashing bound,
properties of single-shot smooth entropies, and the quantum substate theorem -
and also on some newly developed ones. In particular we derive a new bound on
correlations established by local random measurements, and we give a
generalization to the max-entropy of a result of Hastings concerning the
saturation of mutual information in multiparticle systems. The proof can also
be interpreted as providing a limitation on the phenomenon of data hiding in
quantum states.Comment: 35 pages, 6 figures; v2 minor corrections; v3 published versio
On the parameter spectrum of generalized information-entropy measures with no cut-off prescriptions
After studying some properties of the generalized exponential and logarithmic
function, in particular investigating the domain where the first maintains
itself real and positive, and outlining how the known dualities and play an important
role, we shall examine the set of q-deforming parameters that allow generalized
canonical maximum entropy probability distributions (MEPDs) to maintain itself
positive and real without cut-off prescriptions. We determine the set of
q-deforming parameters for which a generalized statistics with discrete but
unbound energy states is possible.Comment: 12 pages, 4 figure
A New Class of Generalized Modified Weibull Distribution with Applications
A new five parameter gamma-generalized modified Weibull (GGMW) distribution which includes exponential, Rayleigh, modified Weibull, Weibull, gamma-modified Weibull, gamma-modified Rayleigh, gamma-modified exponential, gamma-Weibull, gamma-Rayleigh, and gamma-exponential distributions as special cases is proposed and studied. Some mathematical properties of the new class of distributions including moments, distribution of the order statistics, and Renyi entropy are presented. Maximum likelihood estimation technique is used to estimate the model parameters and applications to a real datasets to illustrates the usefulness of the proposed class of models are presented
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