Large N reduction with overlap fermions

We revisit quenched reduction with fermions and explain how some old problems can be avoided using the overlap Dirac operator.Comment: Lattice2002(chiral) 3 pages, no figure

Overlap Fermions on a 20420^4 Lattice

We report results on hadron masses, fitting of the quenched chiral log, and quark masses from Neuberger's overlap fermion on a quenched $20^4$ lattice with lattice spacing $a = 0.15$ fm. We used the improved gauge action which is shown to lower the density of small eigenvalues for $H^2$ as compared to the Wilson gauge action. This makes the calculation feasible on 64 nodes of CRAY-T3E. Also presented is the pion mass on a small volume ($6^3 \times 12$ with a Wilson gauge action at $\beta = 5.7$). We find that for configurations that the topological charge $Q \ne 0$, the pion mass tends to a constant and for configurations with trivial topology, it approaches zero possibly linearly with the quark mass.Comment: Lattice 2000 (Chiral Fermion), 4 pages, 4 figure

Pricing Liquidity Risk with Heterogeneous Investment Horizons

We develop an asset pricing model with stochastic transaction costs and investors with heterogeneous horizons. Depending on their horizon, investors hold different sets of assets in equilibrium. This generates segmentation and spillover effects for expected returns, where the liquidity (risk) premium of illiquid assets is determined by investor horizons and the correlation between liquid and illiquid asset returns. We estimate our model for the cross-section of U.S. stock returns and find that it generates a good fit, mainly due to a combination of a substantial expected liquidity premium and segmentation effects, while the liquidity risk premium is small

Noncompact chiral U(1) gauge theories on the lattice

A new, adiabatic phase choice is adopted for the overlap in the case of an infinite volume, noncompact abelian chiral gauge theory. This gauge choice obeys the same symmetries as the Brillouin-Wigner (BW) phase choice, and, in addition, produces a Wess-Zumino functional that is linear in the gauge variables on the lattice. As a result, there are no gauge violations on the trivial orbit in all theories, consistent and covariant anomalies are simply related and Berry's curvature now appears as a Schwinger term. The adiabatic phase choice can be further improved to produce a perfect phase choice, with a lattice Wess-Zumino functional that is just as simple as the one in continuum. When perturbative anomalies cancel, gauge invariance in the fermionic sector is fully restored. The lattice effective action describing an anomalous abelian gauge theory has an explicit form, close to one analyzed in the past in a perturbative continuum framework.Comment: 35 pages, one figure, plain TeX; minor typos corrected; to appear in PR

A note on Neuberger's double pass algorithm

We analyze Neuberger's double pass algorithm for the matrix-vector multiplication R(H).Y (where R(H) is (n-1,n)-th degree rational polynomial of positive definite operator H), and show that the number of floating point operations is independent of the degree n, provided that the number of sites is much larger than the number of iterations in the conjugate gradient. This implies that the matrix-vector product $(H)^{-1/2} Y \simeq R^{(n-1,n)}(H) \cdot Y$ can be approximated to very high precision with sufficiently large n, without noticeably extra costs. Further, we show that there exists a threshold $n_T$ such that the double pass is faster than the single pass for $n > n_T$, where $n_T \simeq 12 - 25$ for most platforms.Comment: 18 pages, v3: CPU time formulas are obtained, to appear in Physical Review

First quarter bank results: good news, bad news

Banks and banking - West ; Banks and banking - California

Bounds on the Wilson Dirac Operator

New exact upper and lower bounds are derived on the spectrum of the square of the hermitian Wilson Dirac operator. It is hoped that the derivations and the results will be of help in the search for ways to reduce the cost of simulations using the overlap Dirac operator. The bounds also apply to the Wilson Dirac operator in odd dimensions and are therefore relevant to domain wall fermions as well.Comment: 16 pages, TeX, 3 eps figures, small corrections and improvement

Numerical results from large N reduced QCD_2

Some results in QCD_2 at large N are presented using the reduced model on the lattice. Overlap fermions are used to compute meson propagators.Comment: 3 pages, contribution to Lattice 2002, Bosto

A Local Inversion Principle of the Nash-Moser Type

We prove an inverse function theorem of the Nash-Moser type. The main difference between our method and that of [J. Moser, Proc. Nat. Acad. Sci. USA, 47 (1961), pp. 1824-1831] is that we use continuous steepest descent while Moser uses a combination of Newton-type iterations and approximate inverses. We bypass the loss of derivatives problem by working on finite dimensional subspaces of infinitely differentiable functions