11,464 research outputs found
Wealth condensation in a simple model of economy
We introduce a simple model of economy, where the time evolution is described
by an equation capturing both exchange between individuals and random
speculative trading, in such a way that the fundamental symmetry of the economy
under an arbitrary change of monetary units is insured. We investigate a
mean-field limit of this equation and show that the distribution of wealth is
of the Pareto (power-law) type. The Pareto behaviour of the tails of this
distribution appears to be robust for finite range models, as shown using both
a mapping to the random `directed polymer' problem, as well as numerical
simulations. In this context, a transition between an economy dominated by a
few individuals from a situation where the wealth is more evenly spread out, is
found. An interesting outcome is that the distribution of wealth tends to be
very broadly distributed when exchanges are limited, either in amplitude or
topologically. Favoring exchanges (and, less surprisingly, increasing taxes)
seems to be an efficient way to reduce inequalities.Comment: 11 pages, 3 .ps figure
Cavity-induced damping and level shifts in a wide aperture spherical resonator
We calculate explicitly the space dependence of the radiative relaxation
rates and associated level shifts for a dipole placed in the vicinity of the
center of a spherical cavity with a large numerical aperture and a relatively
low finesse. In particular, we give simple and useful analytic formulas for
these quantities, that can be used with arbitrary mirrors transmissions. The
vacuum field in the vicinity of the center of the cavity is actually equivalent
to the one obtained in a microcavity, and this scheme allows one to predict
significant cavity QED effects.Comment: 28 pages, 5 figures. In v2 some references and appendices adde
Correlation structure of extreme stock returns
It is commonly believed that the correlations between stock returns increase
in high volatility periods. We investigate how much of these correlations can
be explained within a simple non-Gaussian one-factor description with time
independent correlations. Using surrogate data with the true market return as
the dominant factor, we show that most of these correlations, measured by a
variety of different indicators, can be accounted for. In particular, this
one-factor model can explain the level and asymmetry of empirical exceedance
correlations. However, more subtle effects require an extension of the one
factor model, where the variance and skewness of the residuals also depend on
the market return.Comment: Substantial rewriting. Added exceedance correlations, removed some
confusing material. To appear in Quantitative Financ
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