2,986 research outputs found
Eigenvalues and Singular Values of Products of Rectangular Gaussian Random Matrices (The Extended Version)
We consider a product of an arbitrary number of independent rectangular
Gaussian random matrices. We derive the mean densities of its eigenvalues and
singular values in the thermodynamic limit, eventually verified numerically.
These densities are encoded in the form of the so called M-transforms, for
which polynomial equations are found. We exploit the methods of planar
diagrammatics, enhanced to the non-Hermitian case, and free random variables,
respectively; both are described in the appendices. As particular results of
these two main equations, we find the singular behavior of the spectral
densities near zero. Moreover, we propose a finite-size form of the spectral
density of the product close to the border of its eigenvalues' domain. Also,
led by the striking similarity between the two main equations, we put forward a
conjecture about a simple relationship between the eigenvalues and singular
values of any non-Hermitian random matrix whose spectrum exhibits rotational
symmetry around zero.Comment: 50 pages, 8 figures, to appear in the Proceedings of the 23rd Marian
Smoluchowski Symposium on Statistical Physics: "Random Matrices, Statistical
Physics and Information Theory," September 26-30, 2010, Krakow, Polan
Facilitating the Decentralised Exchange of Cryptocurrencies in an Order-Driven Market
This article discusses a protocol to facilitate decentralised exchanges on an order-driven market through a consortium of market services operators. We discuss whether this hybrid protocol combining a centralised initiation phase with a decentralised execution phase outperforms fully centralised exchanges with regards to efficiency and security. Here, a fully efficient and fully secure protocol is defined as one where traders incur no trading costs or opportunity costs and counterparty risk is absent. We devise a protocol addressing the main downsides in the decentralised exchange process that uses a facilitating distributed ledger, maintains an order book and monitors the order status in real-time to provide accurate exchange rate information and performance scoring of participants. We show how performance ratings can lower opportunity costs and how a rolling benchmark rate of verifiable trades can be used to establish a trustworthy exchange rate between cryptocurrencies. The formal validation of the proposed technical mechanisms is the subject of future work
Judgments in the Sharing Economy: The Effect of User-Generated Trust and Reputation Information on Decision-Making Accuracy and Bias
The growing ecosystem of peer-to-peer enterprise â the Sharing Economy (SE) â has
brought with it a substantial change in how we access and provide goods and services.
Within the SE, individuals make decisions based mainly on user-generated trust and
reputation information (TRI). Recent research indicates that the use of such information
tends to produce a positivity bias in the perceived trustworthiness of fellow users.
Across two experimental studies performed on an artificial SE accommodation platform,
we test whether usersâ judgments can be accurate when presented with diagnostic
information relating to the quality of the profiles they see or if these overly positive
perceptions persist. In study 1, we find that users are quite accurate overall (70%)
at determining the quality of a profile, both when presented with full profiles or with
profiles where they selected three TRI elements they considered useful for their decisionmaking. However, users tended to exhibit an âupward quality biasâ when making errors.
In study 2, we leveraged patterns of frequently vs. infrequently selected TRI elements
to understand whether users have insights into which are more diagnostic and find
that presenting frequently selected TRI elements improved usersâ accuracy. Overall, our
studies demonstrate that â positivity bias notwithstanding â users can be remarkably
accurate in their online SE judgments
Financial instability from local market measures
We study the emergence of instabilities in a stylized model of a financial
market, when different market actors calculate prices according to different
(local) market measures. We derive typical properties for ensembles of large
random markets using techniques borrowed from statistical mechanics of
disordered systems. We show that, depending on the number of financial
instruments available and on the heterogeneity of local measures, the market
moves from an arbitrage-free phase to an unstable one, where the complexity of
the market - as measured by the diversity of financial instruments - increases,
and arbitrage opportunities arise. A sharp transition separates the two phases.
Focusing on two different classes of local measures inspired by real markets
strategies, we are able to analytically compute the critical lines,
corroborating our findings with numerical simulations.Comment: 17 pages, 4 figure
Eigenvalues and Singular Values of Products of Rectangular Gaussian Random Matrices
We derive exact analytic expressions for the distributions of eigenvalues and
singular values for the product of an arbitrary number of independent
rectangular Gaussian random matrices in the limit of large matrix dimensions.
We show that they both have power-law behavior at zero and determine the
corresponding powers. We also propose a heuristic form of finite size
corrections to these expressions which very well approximates the distributions
for matrices of finite dimensions.Comment: 13 pages, 3 figure
Asymmetric correlation matrices: an analysis of financial data
We analyze the spectral properties of correlation matrices between distinct
statistical systems. Such matrices are intrinsically non symmetric, and lend
themselves to extend the spectral analyses usually performed on standard
Pearson correlation matrices to the realm of complex eigenvalues. We employ
some recent random matrix theory results on the average eigenvalue density of
this type of matrices to distinguish between noise and non trivial correlation
structures, and we focus on financial data as a case study. Namely, we employ
daily prices of stocks belonging to the American and British stock exchanges,
and look for the emergence of correlations between two such markets in the
eigenvalue spectrum of their non symmetric correlation matrix. We find several
non trivial results, also when considering time-lagged correlations over short
lags, and we corroborate our findings by additionally studying the asymmetric
correlation matrix of the principal components of our datasets.Comment: Revised version; 11 pages, 13 figure
Dual-readout Calorimetry
The RD52 Project at CERN is a pure instrumentation experiment whose goal is
to understand the fundamental limitations to hadronic energy resolution, and
other aspects of energy measurement, in high energy calorimeters. We have found
that dual-readout calorimetry provides heretofore unprecedented information
event-by-event for energy resolution, linearity of response, ease and
robustness of calibration, fidelity of data, and particle identification,
including energy lost to binding energy in nuclear break-up. We believe that
hadronic energy resolutions of {\sigma}/E 1 - 2% are within reach for
dual-readout calorimeters, enabling for the first time comparable measurement
preci- sions on electrons, photons, muons, and quarks (jets). We briefly
describe our current progress and near-term future plans. Complete information
on all aspects of our work is available at the RD52 website
http://highenergy.phys.ttu.edu/dream/.Comment: 10 pages, 10 figures, Snowmass White pape
Hadron detection with a dual-readout fiber calorimeter
In this paper, we describe measurements of the response functions of a
fiber-based dual- readout calorimeter for pions, protons and multiparticle
"jets" with energies in the range from 10 to 180 GeV. The calorimeter uses lead
as absorber material and has a total mass of 1350 kg. It is complemented by
leakage counters made of scintillating plastic, with a total mass of 500 kg.
The effects of these leakage counters on the calorimeter performance are
studied as well. In a separate section, we investigate and compare different
methods to measure the energy resolution of a calorimeter. Using only the
signals provided by the calorimeter, we demonstrate that our dual-readout
calorimeter, calibrated with electrons, is able to reconstruct the energy of
proton and pion beam particles to within a few percent at all energies. The
fractional widths of the signal distributions for these particles (sigma/E)
scale with the beam energy as 30%/sqrt(E), without any additional contributing
terms
Accounting for risk of non linear portfolios: a novel Fourier approach
The presence of non linear instruments is responsible for the emergence of
non Gaussian features in the price changes distribution of realistic
portfolios, even for Normally distributed risk factors. This is especially true
for the benchmark Delta Gamma Normal model, which in general exhibits
exponentially damped power law tails. We show how the knowledge of the model
characteristic function leads to Fourier representations for two standard risk
measures, the Value at Risk and the Expected Shortfall, and for their
sensitivities with respect to the model parameters. We detail the numerical
implementation of our formulae and we emphasizes the reliability and efficiency
of our results in comparison with Monte Carlo simulation.Comment: 10 pages, 12 figures. Final version accepted for publication on Eur.
Phys. J.
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