The space of generically \'etale families

We construct a space $G^n_X$ and a rank $n$, generically etale family of closed subspaces in a separated ambient space $X$. The constructed pair satisfies a universal property of generically etale families of closed subspaces in $X$. This universal property is derived directly from the construction and does in particular not use the Hilbert scheme. The constructed space $G^n_X$ is by its universal property canonically identified with a closed subspace of the Hilbert scheme.Comment: 28 pages; replaced $TS^{n-1} R\otimes R$ with $TS^{n-1,1} R$; simplified some proof

Self-consistent theory of many-body localisation in a quantum spin chain with long-range interactions

Many-body localisation is studied in a disordered quantum spin-1/2 chain with long-ranged power-law interactions, and distinct power-law exponents for interactions between longitudinal and transverse spin components. Using a self-consistent mean-field theory centring on the local propagator in Fock space and its associated self-energy, a localisation phase diagram is obtained as a function of the power-law exponents and the disorder strength of the random fields acting on longitudinal spin-components. Analytical results are corroborated using the well-studied and complementary numerical diagnostics of level statistics, entanglement entropy, and participation entropy, obtained via exact diagonalisation. We find that increasing the range of interactions between transverse spin components hinders localisation and enhances the critical disorder strength. In marked contrast, increasing the interaction range between longitudinal spin components is found to enhance localisation and lower the critical disorder.Comment: 30 pages, 4 figure

Real Exchange Rate Misalignment: Prelude to Crisis?

A model of the long run equilibrium real exchange rate based upon macroeconomic fundamentals is employed to calculate real exchange rate misalignments for Poland and Russia during the 1990s using the Beveridge and Nelson (1981) decomposition of macrofundamentals into transitory and permanent components. Short run movements of the real exchange rate are estimated with ARIMA and GARCH error correction specifications. The different nominal exchange rate regimes of the two countries generate different levels of misalignment and different responses to exogenous shocks. The average misalignment in Russia is substantially greater than that in Poland, indicating incipient pressures to devalue the ruble immediately preceding the August 1998 crisis. The half life of an exogenous shock is found to be much shorter for Poland than for Russia in the pre-crisis period. Dynamic forecasts indicate that the movements of the real exchange rate in the post-crisis period are significantly different from those in the pre-crisis period. Thus, the currency crisis in Russia could not be anticipated with the movements of the real exchange rate estimated with the macroeconomic fundamentals.http://deepblue.lib.umich.edu/bitstream/2027.42/40183/3/wp797.pd