17,004 research outputs found
Chiral limit of the two-dimensional fermionic determinant in a general magnetic field
We consider the effective action for massive two-dimensional QED in flat
Euclidean space-time in the background of a general square-integrable magnetic
field with finite range. It is shown that its small mass limit is controlled by
the chiral anomaly. New results for the low-energy scattering of electrons in
2+1 dimensions in static, inhomogenous magnetic fields are also presented.Comment: The interpretation of Eq.(2.14) is elucidate
Towards breaking the Omega-bias degeneracy in density--velocity comparisons
I derive a second-order local relation between the REDSHIFT-space mass
density field and the REAL-space velocity field. This relation can be useful
for comparisons between the cosmic density and peculiar velocity fields, for a
number of reasons. First, relating the real-space velocity directly to the
redshift-space density enables one to avoid the Omega-dependent reconstruction
of the density field in real space. Secondly, the reconstruction of the
three-dimensional velocity field in redshift space, questionable because of its
vorticity, is also unnecessary. Finally, a similar relation between the GALAXY
density field and the velocity field offers a way to break the Omega-bias
degeneracy in density--velocity comparisons, when combined with an additional
measurement of the redshift-space galaxy skewness. I derive the latter relation
under the assumption of nonlinear but local bias; accounting for stochasticity
of bias is left for further study.Comment: 13 pages, no figures, uses mn.sty. The calculation properly redone
for bias in real space, added references. Accepted by MNRA
Statistical modelling of financial crashes: Rapid growth, illusion of certainty and contagion
We develop a rational expectations model of financial bubbles and study ways in which a generic risk-return interplay is incorporated into prices. We retain the interpretation of the leading Johansen-Ledoit-Sornette model, namely, that the price must rise prior to a crash in order to compensate a representative investor for the level of risk. This is accompanied, in our stochastic model, by an illusion of certainty as described by a decreasing volatility function. The basic model is then extended to incorporate multivariate bubbles and contagion, non-Gaussian models and models based on stochastic volatility. Only in a stochastic volatility model where the mean of the log-returns is considered fixed does volatility increase prior to a crash.Financial crashes, super-exponential growth, illusion of certainty, contagion, housing-bubble.
Statistical modelling of financial crashes: Rapid growth, illusion of certainty and contagion
We develop a rational expectations model of financial bubbles and study ways in which a generic risk-return interplay is incorporated into prices. We retain the interpretation of the leading Johansen-Ledoit-Sornette model, namely, that the price must rise prior to a crash in order to compensate a representative investor for the level of risk. This is accompanied, in our stochastic model, by an illusion of certainty as described by a decreasing volatility function. The basic model is then extended to incorporate multivariate bubbles and contagion, non-Gaussian models and models based on stochastic volatility. Only in a stochastic volatility model where the mean of the log-returns is fixed does volatility increase prior to a crash.financial crashes; super-exponential growth; illusion of certainty; contagion
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