2,571 research outputs found
Superdiffusivity of asymmetric exclusion process in dimensions one and two
We prove that the diffusion coefficient for the asymmetric exclusion process
diverges at least as fast as in dimension and
in . The method applies to nearest and non-nearest neighbor asymmetric
exclusion processes
A Note on ODEs from Mirror Symmetry
We give close formulas for the counting functions of rational curves on
complete intersection Calabi-Yau manifolds in terms of special solutions of
generalized hypergeometric differential systems. For the one modulus cases we
derive a differential equation for the Mirror map, which can be viewed as a
generalization of the Schwarzian equation. We also derive a nonlinear seventh
order differential equation which directly governs the instanton corrected
Yukawa coupling.Comment: 24 pages using harvma
Zooming in on local level statistics by supersymmetric extension of free probability
We consider unitary ensembles of Hermitian NxN matrices H with a confining
potential NV where V is analytic and uniformly convex. From work by
Zinn-Justin, Collins, and Guionnet and Maida it is known that the large-N limit
of the characteristic function for a finite-rank Fourier variable K is
determined by the Voiculescu R-transform, a key object in free probability
theory. Going beyond these results, we argue that the same holds true when the
finite-rank operator K has the form that is required by the Wegner-Efetov
supersymmetry method of integration over commuting and anti-commuting
variables. This insight leads to a potent new technique for the study of local
statistics, e.g., level correlations. We illustrate the new technique by
demonstrating universality in a random matrix model of stochastic scattering.Comment: 38 pages, 3 figures, published version, minor changes in Section
Standard model plethystics
We study the vacuum geometry prescribed by the gauge invariant operators of the minimal supersymmetric standard model via the plethystic program. This is achieved by using several tricks to perform the highly computationally challenging Molien-Weyl integral, from which we extract the Hilbert series, encoding the invariants of the geometry at all degrees. The fully refined Hilbert series is presented as the explicit sum of 1422 rational functions. We found a good choice of weights to unrefine the Hilbert series into a rational function of a single variable, from which we can read off the dimension and the degree of the vacuum moduli space of the minimal supersymmetric standard model gauge invariants. All data in Mathematica format are also presented
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