26,411 research outputs found
WZW fusion rings in the limit of infinite level
We show that the WZW fusion rings at finite levels form a projective system
with respect to the partial ordering provided by divisibility of the height,
i.e. the level shifted by a constant. From this projective system we obtain WZW
fusion rings in the limit of infinite level. This projective limit constitutes
a mathematically well-defined prescription for the `classical limit' of WZW
theories which replaces the naive idea of `sending the level to infinity'. The
projective limit can be endowed with a natural topology, which plays an
important role for studying its structure. The representation theory of the
limit can be worked out by considering the associated fusion algebra; this way
we obtain in particular an analogue of the Verlinde formula.Comment: Latex2e, 31 pages (A4
Fermi Surface of the 2D Hubbard Model at Weak Coupling
We calculate the interaction-induced deformation of the Fermi surface in the
two-dimensional Hubbard model within second order perturbation theory. Close to
half-filling, interactions enhance anisotropies of the Fermi surface, but they
never modify the topology of the Fermi surface in the weak coupling regime.Comment: 4 pages, LaTeX2e, 5 embedded EPS figures, accepted to be published in
Z. Phys.
The dynamics of the leverage cycle
We present a simple agent-based model of a financial system composed of
leveraged investors such as banks that invest in stocks and manage their risk
using a Value-at-Risk constraint, based on historical observations of asset
prices. The Value-at-Risk constraint implies that when perceived risk is low,
leverage is high and vice versa, a phenomenon that has been dubbed pro-cyclical
leverage. We show that this leads to endogenous irregular oscillations, in
which gradual increases in stock prices and leverage are followed by drastic
market collapses, i.e. a leverage cycle. This phenomenon is studied using
simplified models that give a deeper understanding of the dynamics and the
nature of the feedback loops and instabilities underlying the leverage cycle.
We introduce a flexible leverage regulation policy in which it is possible to
continuously tune from pro-cyclical to countercyclical leverage. When the
policy is sufficiently countercyclical and bank risk is sufficiently low the
endogenous oscillation disappears and prices go to a fixed point. While there
is always a leverage ceiling above which the dynamics are unstable,
countercyclical leverage can be used to raise the ceiling. We also study the
impact on leverage cycles of direct, temporal control of the bank's riskiness
via the bank's required Value-at-Risk quantile. Under such a rule the regulator
relaxes the Value-at-Risk quantile following a negative stock price shock and
tightens it following a positive shock. While such a policy rule can reduce the
amplitude of leverage cycles, its effectiveness is highly dependent on the
choice of parameters. Finally, we investigate fixed limits on leverage and show
how they can control the leverage cycle.Comment: 35 pages, 9 figure
Comment on "Separability of quantum states and the violation of Bell-type inequalities"
The statement of E.R. Loubenets, Phys. Rev. A 69, 042102 (2004), that
separable states can violate classical probabilistic constraints is based on a
misleading definition of classicality, which is much narrower than Bell's
concept of local hidden variables. In a Bell type setting the notion of
classicality used by Loubenets corresponds to the assumption of perfect
correlations if the same observable is measured on both sides. While it is
obvious that most separable states do not satisfy this assumption, this does
not constitute "non-classical" behaviour in any usual sense of the word.Comment: 1 page, accepted by Phys. Rev.
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