92 research outputs found
Stability of the replica-symmetric saddle-point in general mean-field spin-glass models
Within the replica approach to mean-field spin-glasses the transition from
ergodic high-temperature behaviour to the glassy low-temperature phase is
marked by the instability of the replica-symmetric saddle-point. For general
spin-glass models with non-Gaussian field distributions the corresponding
Hessian is a matrix with the number of replicas tending to
zero eventually. We block-diagonalize this Hessian matrix using representation
theory of the permutation group and identify the blocks related to the
spin-glass susceptibility. Performing the limit within these blocks we
derive expressions for the de~Almeida-Thouless line of general spin-glass
models. Specifying these expressions to the cases of the
Sherrington-Kirkpatrick, Viana-Bray, and the L\'evy spin glass respectively we
obtain results in agreement with previous findings using the cavity approach
Alternation of different fluctuation regimes in the stock market dynamics
Based on the tick-by-tick stock prices from the German and American stock
markets, we study the statistical properties of the distribution of the
individual stocks and the index returns in highly collective and noisy
intervals of trading, separately. We show that periods characterized by the
strong inter-stock couplings can be associated with the distributions of index
fluctuations which reveal more pronounced tails than in the case of weaker
couplings in the market. During periods of strong correlations in the German
market these distributions can even reveal an apparent L\'evy-stable component.Comment: 19 page
Noise Dressing of Financial Correlation Matrices
We show that results from the theory of random matrices are potentially of
great interest to understand the statistical structure of the empirical
correlation matrices appearing in the study of price fluctuations. The central
result of the present study is the remarkable agreement between the theoretical
prediction (based on the assumption that the correlation matrix is random) and
empirical data concerning the density of eigenvalues associated to the time
series of the different stocks of the S&P500 (or other major markets). In
particular the present study raises serious doubts on the blind use of
empirical correlation matrices for risk management.Comment: Latex (Revtex) 3 pp + 2 postscript figures (in-text
Quantifying dynamics of the financial correlations
A novel application of the correlation matrix formalism to study dynamics of
the financial evolution is presented. This formalism allows to quantify the
memory effects as well as some potential repeatable intradaily structures in
the financial time-series. The present study is based on the high-frequency
Deutsche Aktienindex (DAX) data over the time-period between November 1997 and
December 1999 and demonstrates a power of the method. In this way two
significant new aspects of the DAX evolution are identified: (i) the memory
effects turn out to be sizably shorter than what the standard autocorrelation
function analysis seems to indicate and (ii) there exist short term repeatable
structures in fluctuations that are governed by a distinct dynamics. The former
of these results may provide an argument in favour of the market efficiency
while the later one may indicate origin of the difficulty in reaching a
Gaussian limit, expected from the central limit theorem, in the distribution of
returns on longer time-horizons.Comment: 10 pages, 7 PostScript figures, talk presented by the first Author at
the NATO ARW on Econophysics, Prague, February 8-10, 2001; to be published in
proceedings (Physica A
Possible Stratification Mechanism in Granular Mixtures
We propose a mechanism to explain what occurs when a mixture of grains of
different sizes and different shapes (i.e. different repose angles) is poured
into a quasi-two-dimensional cell. Specifically, we develop a model that
displays spontaneous stratification of the large and small grains in
alternating layers. We find that the key requirement for stratification is a
difference in the repose angles of the two pure species, a prediction confirmed
by experimental findings. We also identify a kink mechanism that appears to
describe essential aspects of the dynamics of stratification.Comment: 4 pages, 4 figures, http://polymer.bu.edu/~hmakse/Home.htm
Domain size effects in Barkhausen noise
The possible existence of self-organized criticality in Barkhausen noise is
investigated theoretically through a single interface model, and experimentally
from measurements in amorphous magnetostrictive ribbon Metglas 2605TCA under
stress. Contrary to previous interpretations in the literature, both simulation
and experiment indicate that the presence of a cutoff in the avalanche size
distribution may be attributed to finite size effects.Comment: 5 pages, 3 figures, submitted so Physical Review
Analytic computation of the Instantaneous Normal Modes spectrum in low density liquids
We analytically compute the spectrum of the Hessian of the Hamiltonian for a
system of N particles interacting via a purely repulsive potential in one
dimension. Our approach is valid in the low density regime, where we compute
the exact spectrum also in the localized sector. We finally perform a numerical
analysis of the localization properties of the eigenfunctions.Comment: 4 RevTeX pages, 4 EPS figures. Revised version to appear on Phys.
Rev. Let
The phase diagram of L\'evy spin glasses
We study the L\'evy spin-glass model with the replica and the cavity method.
In this model each spin interacts through a finite number of strong bonds and
an infinite number of weak bonds. This hybrid behaviour of L\'evy spin glasses
becomes transparent in our solution: the local field contains a part
propagating along a backbone of strong bonds and a Gaussian noise term due to
weak bonds. Our method allows to determine the complete replica symmetric phase
diagram, the replica symmetry breaking line and the entropy. The results are
compared with simulations and previous calculations using a Gaussian ansatz for
the distribution of fields.Comment: 20 pages, 7 figure
Size Segregation of Granular Matter in Silo Discharges
We present an experimental study of segregation of granular matter in a
quasi-two dimensional silo emptying out of an orifice. Size separation is
observed when multi-sized particles are used with the larger particles found in
the center of the silo in the region of fastest flow. We use imaging to study
the flow inside the silo and quantitatively measure the concentration profiles
of bi-disperse beads as a function of position and time. The angle of the
surface is given by the angle of repose of the particles, and the flow occurs
in a few layers only near the top of this inclined surface. The flowing region
becomes deeper near the center of the silo and is confined to a parabolic
region centered at the orifice which is approximately described by the
kinematic model. The experimental evidence suggests that the segregation occurs
on the surface and not in the flow deep inside the silo where velocity
gradients also are present. We report the time development of the
concentrations of the bi-disperse particles as a function of size ratios, flow
rate, and the ratio of initial mixture. The qualitative aspects of the observed
phenomena may be explained by a void filling model of segregation.Comment: 6 pages, 10 figures (gif format), postscript version at
http://physics.clarku.edu/~akudrolli/nls.htm
Elements for a Theory of Financial Risks
Estimating and controlling large risks has become one of the main concern of
financial institutions. This requires the development of adequate statistical
models and theoretical tools (which go beyond the traditionnal theories based
on Gaussian statistics), and their practical implementation. Here we describe
three interrelated aspects of this program: we first give a brief survey of the
peculiar statistical properties of the empirical price fluctuations. We then
review how an option pricing theory consistent with these statistical features
can be constructed, and compared with real market prices for options. We
finally argue that a true `microscopic' theory of price fluctuations (rather
than a statistical model) would be most valuable for risk assessment. A simple
Langevin-like equation is proposed, as a possible step in this direction.Comment: 22 pages, to appear in `Order, Chance and Risk', Les Houches (March
1998), to be published by Springer/EDP Science
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