1,578 research outputs found
Weighted Fixed Points in Self-Similar Analysis of Time Series
The self-similar analysis of time series is generalized by introducing the
notion of scenario probabilities. This makes it possible to give a complete
statistical description for the forecast spectrum by defining the average
forecast as a weighted fixed point and by calculating the corresponding a
priori standard deviation and variance coefficient. Several examples of
stock-market time series illustrate the method.Comment: two additional references are include
Self-similar approach to market analysis
A novel approach to analyzing time series generated by complex systems, such
as markets, is presented. The basic idea of the approach is the {\it Law of
Self-Similar Evolution}, according to which any complex system develops
self-similarly. There always exist some internal laws governing the evolution
of a system, say of a market, so that each of such systems possesses its own
character regulating its behaviour. The problem is how to discover these hidden
internal laws defining the system character. This problem can be solved by
employing the {\it Self-Similar Approximation Theory}, which supplies the
mathematical foundation for the Law of Self-Similar Evolution. In this report,
the theoretical basis of the new approach to analyzing time series is
formulated, with an accurate explanation of its principal points.Comment: Latex file, 17 pages, no figure
Thermalization and pseudolocality in extended quantum systems
Recently, it was understood that modified concepts of locality played an
important role in the study of extended quantum systems out of equilibrium, in
particular in so-called generalized Gibbs ensembles. In this paper, we
rigorously study pseudolocal charges and their involvement in time evolutions
and in the thermalization process of arbitrary states with strong enough
clustering properties. We show that the densities of pseudolocal charges form a
Hilbert space, with inner product determined by thermodynamic susceptibilities.
Using this, we define the family of pseudolocal states, which are determined by
pseudolocal charges. This family includes thermal Gibbs states at high enough
temperatures, as well as (a precise definition of) generalized Gibbs ensembles.
We prove that the family of pseudolocal states is preserved by finite time
evolution, and that, under certain conditions, the stationary state emerging at
infinite time is a generalized Gibbs ensemble with respect to the evolution
dynamics. If the evolution dynamics does not admit any conserved pseudolocal
charges other than the evolution Hamiltonian, we show that any stationary
pseudolocal state with respect to this dynamics is a thermal Gibbs state, and
that Gibbs thermalization occurs. The framework is that of
translation-invariant states on hypercubic quantum lattices of any
dimensionality (including quantum chains) and finite-range Hamiltonians, and
does not involve integrability.Comment: v1: 43 pages. v2: corrections and clarifications, references added,
46 pages. v3: 48 pages, further corrections made, accepted for publication in
Commun. Math. Phy
The Single Server Queue and the Storage Model: Large Deviations and Fixed Points
We consider the coupling of a single server queue and a storage model defined
as a Queue/Store model in Draief et al. 2004. We establish that if the input
variables, arrivals at the queue and store, satisfy large deviations principles
and are linked through an {\em exponential tilting} then the output variables
(departures from each system) satisfy large deviations principles with the same
rate function. This generalizes to the context of large deviations the
extension of Burke's Theorem derived in Draief et al. 2004.Comment: 20 page
The Measure-theoretic Identity Underlying Transient Fluctuation Theorems
We prove a measure-theoretic identity that underlies all transient
fluctuation theorems (TFTs) for entropy production and dissipated work in
inhomogeneous deterministic and stochastic processes, including those of Evans
and Searles, Crooks, and Seifert. The identity is used to deduce a tautological
physical interpretation of TFTs in terms of the arrow of time, and its
generality reveals that the self-inverse nature of the various trajectory and
process transformations historically relied upon to prove TFTs, while necessary
for these theorems from a physical standpoint, is not necessary from a
mathematical one. The moment generating functions of thermodynamic variables
appearing in the identity are shown to converge in general only in a vertical
strip in the complex plane, with the consequence that a TFT that holds over
arbitrary timescales may fail to give rise to an asymptotic fluctuation theorem
for any possible speed of the corresponding large deviation principle. The case
of strongly biased birth-death chains is presented to illustrate this
phenomenon. We also discuss insights obtained from our measure-theoretic
formalism into the results of Saha et. al. on the breakdown of TFTs for driven
Brownian particles
Combinatorial quantisation of Euclidean gravity in three dimensions
In the Chern-Simons formulation of Einstein gravity in 2+1 dimensions the
phase space of gravity is the moduli space of flat G-connections, where G is a
typically non-compact Lie group which depends on the signature of space-time
and the cosmological constant. For Euclidean signature and vanishing
cosmological constant, G is the three-dimensional Euclidean group. For this
case the Poisson structure of the moduli space is given explicitly in terms of
a classical r-matrix. It is shown that the quantum R-matrix of the quantum
double D(SU(2)) provides a quantisation of that Poisson structure.Comment: cosmetic chang
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