| 1. |
- Andersson, Per-Johan, et al.
(author)
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Power mapping and noise reduction for financial correlations
- 2005
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In: Acta Physica Polonica, Series B. - 0587-4254. ; 36:9, s. 2611-2619
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Conference paper (peer-reviewed)abstract
- The spectral properties of financial correlation matrices can show features known from completely random matrices. A major reason is noise originating from the finite lengths of the financial time series used to compute the correlation matrix elements. In recent years, various methods have been proposed to reduce this noise, i.e. to clean the correlation matrices. This is of direct practical relevance for risk management in portfolio optimization. In this contribution, we discuss in detail the power mapping, a new shrinkage method. We show that the relevant parameter is, to a certain extent, self-determined. Due to the "chirality" and the normalization of the correlation matrix, the optimal shrinkage parameter is fixed. We apply the power mapping and the well-known filtering method, to market data and compare them by optimizing stock portfolios. We address the rle of constraints by excluding short selling in the optimization.
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| 2. |
- Dietz, B, et al.
(author)
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Strength distributions and symmetry breaking in coupled microwave billiards
- 2006
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In: Physical Review Letters. - 1079-7114. ; 96:25
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Journal article (peer-reviewed)abstract
- Flat microwave cavities can be used to experimentally simulate quantum mechanical systems. By coupling two such cavities, we study the equivalent to symmetry breaking in quantum mechanics. As the coupling is tunable, we can measure resonance strength distributions as a function of the symmetry breaking. We analyze the data by employing a qualitative model based on random matrix theory and show that the results derived from the strength distribution are consistent with those previously obtained from spectral statistics.
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| 3. |
- Enders, J, et al.
(author)
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Electric dipole strength below the giant dipole resonance
- 2005
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In: Acta Physica Polonica. Series B: Elementary Particle Physics, Nuclear Physics, Statistical Physics, Theory of Relativity, Field Theory. - 0587-4254. ; 36:4, s. 1077-1087
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Journal article (peer-reviewed)abstract
- Recent experimental findings and theoretical approaches to the electric dipole (El) strength distribution below the particle emission threshold at shell closures are revisited. Results from photon scattering experiments are discussed and compared to predictions within the quasiparticle-phonon nuclear model. An analysis of the fine structure of the El strength is presented. Recent studies of the E1 response of light exotic nuclei are also discussed.
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| 4. |
- Enders, J, et al.
(author)
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Spectral statistics and the fine structure of the electric pygmy dipole resonance in N=82 nuclei
- 2004
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In: Nuclear Physics, Section A. - : Elsevier BV. - 0375-9474. ; 741, s. 3-28
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Journal article (peer-reviewed)abstract
- We study the statistical properties of the electric pygmy dipole resonance in four different isotones with neutron number N = 82. These nuclei are Ba-138(56), Ce-140(58), Nd-142(60), (144)(62)sm. The data set comprises levels with spin and parity J(pi) = 1(-) and their ground state B(E1) transition strengths. The statistics are found to be "mixed", i.e., in between the predictions of random matrix theory for correlated and uncorrelated spectra. Moreover, we calculate spectra and transition strengths in the quasiparticle phonon model (QPM). We compare experimental and theoretical findings. The incompleteness of the data sets and its impact on the results is discussed. A consistent picture emerges which yields an improved understanding of the statistical properties of the pygmy resonance. (
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| 5. |
- Grönqvist, Johan, et al.
(author)
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Energy localization in two chaotically coupled systems
- 2005
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In: Physical Review E. - 1063-651X. ; 71:3, Part A
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Journal article (peer-reviewed)abstract
- We set up and analyze a random matrix model to study energy localization and its time behavior in two chaotically coupled systems. This investigation is prompted by a recent experimental and theoretical study of Weaver and Lobkis on coupled elastomechanical systems. Our random matrix model properly describes the main features of the findings by Weaver and Lobkis. Due to its general character, our model is also applicable to similar systems in other areas of physics-for example, to chaotically coupled quantum dots.
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| 6. |
- Grönqvist, Johan, et al.
(author)
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Strain in semiconductor core-shell nanowires
- 2009
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In: Applied Physics Reviews. - : AIP Publishing. - 1931-9401. ; 106:5
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Journal article (peer-reviewed)abstract
- We compute strain distributions in core-shell nanowires of zinc blende structure. We use both continuum elasticity theory and an atomistic model, and consider both finite and infinite wires. The atomistic valence force-field (VFF) model has only few assumptions. But it is less computationally efficient than the finite-element (FE) continuum elasticity model. The generic properties of the strain distributions in core-shell nanowires obtained based on the two models agree well. This agreement indicates that although the calculations based on the VFF model are computationally feasible in many cases, the continuum elasticity theory suffices to describe the strain distributions in large core-shell nanowire structures. We find that the obtained strain distributions for infinite wires are excellent approximations to the strain distributions in finite wires, except in the regions close to the ends. Thus, our most computationally efficient model, the FE continuum elasticity model developed for infinite wires, is sufficient, unless edge effects are important. We give a comprehensive discussion of strain profiles. We find that the hydrostatic strain in the core is dominated by the axial strain-component, epsilon(ZZ). We also find that although the individual strain components have a complex structure, the hydrostatic strain shows a much simpler structure. All in-plane strain components are of similar magnitude. The nonplanar off-diagonal strain components (epsilon(XZ) and epsilon(YZ)) are small but nonvanishing. Thus the material is not only stretched and compressed but also warped. The models used can be extended for the study of wurtzite nanowire structures, as well as nanowires with multiple shells.
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| 7. |
- Grönqvist, Johan, et al.
(author)
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The k-point random matrix kernels obtained from one-point supermatrix models
- 2004
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In: Journal of Physics A: Mathematical and General. - : IOP Publishing. - 0305-4470 .- 1361-6447. ; 37:6, s. 2331-2344
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Journal article (peer-reviewed)abstract
- The k-point correlation functions of the Gaussian random matrix ensembles are certain determinants of functions which depend on only two arguments. They are referred to as kernels, since they are the building blocks of all correlations. We show that the kernels are obtained, for arbitrary level number, directly from supermatrix models for one-point functions. More precisely, the generating functions of the one-point functions are equivalent to the kernels. This is surprising, because it implies that already the one-point generating function holds essential information about the k-point correlations. This also establishes a link to the averaged ratios of spectral determinants, i.e. of characteristic polynomials.
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| 8. |
- Guhr, Thomas, et al.
(author)
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A certain localization effect in coupled systems and messages from the crystal sphere
- 2005
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In: AIP Conference Proceedings. - : AIP. - 0094-243X .- 1551-7616. ; 777, s. 160-170
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Conference paper (peer-reviewed)abstract
- Two theoretical studies are presented, both prompted by recent experiments. First, we investigate the time evolution of excitations in two chaotically coupled systems. There is a certain localization effect, because equipartition of the probability density or the energy is typically not reached. We use a random matrix model to give a generic explanation for this effect. Second, we derive a leading order Weyl formula for the elastic vibration spectrum of anisotropic quartz. This is non-trivial due to the presence of different modes. We discuss a duality between one spherical billiard with anisotropy in configuration space and three non-spherical billiards without anisotropy in slowness space
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| 9. |
- Guhr, Thomas, et al.
(author)
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A new method to estimate the noise in financial correlation matrices
- 2003
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In: Journal of Physics A: Mathematical and General. - : IOP Publishing. - 0305-4470. ; 36:12, s. 3009-3032
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Journal article (peer-reviewed)abstract
- Companies belonging to the same industrial branch are subject to similar economical influences. Hence, the time series of their stocks can show similar trends implying a correlation. Financial correlation matrices measure the unsystematic correlations between time series of stocks. Such information is important for risk management. It has been found by Laloux et al that the correlation matrices are 'noise dressed', a major reason being the finiteness of the time series. We present a new and alternative method to estimate this noise. We introduce a power mapping of the elements in the correlation matrix which suppresses the noise and thereby effectively 'prolongs' the time series. Neither further data processing nor additional input is needed. To develop and test our method, we use a model suggested by Noh which can be viewed as a special case of a 'factor model' in economics. We perform numerical simulations for the time series and obtain correlation matrices. We support the numerics by a qualitative analytical discussion. With our approach, different correlation structures buried under this noise can be detected. Our method is general and can be applied to all systems in which time series are measured.
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| 10. |
- Guhr, Thomas, et al.
(author)
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A supersymmetry approach to billiards with randomly distributed scatterers: II. Correlations
- 2004
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In: Journal of Physics A: Mathematical and General. - : IOP Publishing. - 0305-4470 .- 1361-6447. ; 37:6, s. 2175-2190
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Journal article (peer-reviewed)abstract
- In a previous contribution (Stockmann H J 2002 J. Phys. A: Math. Gen. 35 5165), the density of states was calculated for a billiard with randomly distributed delta-like scatterers, doubly averaged over the positions of the impurities and the billiard shape. This result is now extended to the k-point correlation function. Using supersymmetric methods, we show that the correlations in the bulk are always identical to those of the Gaussian unitary ensemble (GUE) of random matrices. In passing from the band centre to the tail states, the density of states is depleted considerably and the two-point correlation function shows a gradual change from the GUE behaviour to that found for completely uncorrelated eigenvalues. This can be viewed as similar to a mobility edge.
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