Ehrhart h∗h^*-vectors of hypersimplices

We consider the Ehrhart $h^*$-vector for the hypersimplex. It is well-known that the sum of the $h_i^*$ is the normalized volume which equals an Eulerian numbers. The main result is a proof of a conjecture by R. Stanley which gives an interpretation of the $h^*_i$ coefficients in terms of descents and excedances. Our proof is geometric using a careful book-keeping of a shelling of a unimodular triangulation. We generalize this result to other closely related polytopes

A modified BFKL equation with unitarity

We propose a modified Balitskii-Fadin-Kuraev-Lipatov equation from the viewpoint of the resummation technique, which satisfies the unitarity bound. The idea is to relax the strong rapidity ordering and to restrict phase space for real gluon emissions in the evaluation of the BFKL kernel. It is found that the gluon distribution function rises as a power of the Bjorken variable $x$, and then saturates at $x\to 0$. We estimate that the saturation begins to occur for $x< 10^{-4}$.Comment: Conclusion is revised. One figure is adde

The Implied Benchmark Rate in the Credit Default Swap Market of Sovereign Bonds

Credit default swap(CDS) is a new developed derivative to insure the credit risk of an underlying entity. This paper investigates the correlation relationship of the CDS market of sovereign borrowers and sovereign bond market. Applying the formula in the paper of Hull et al.(2004), an implied default-free rate(also called benchmark rate) of CDS market is computed; its correlations with US treasury and LIBOR are tested respectively. The tests indicate that,in sovereign CDS market, the benchmark is more related with US treasury, although LIBOR has been used as the best approximation of market benchmark in both academia and industry. Therefore, this paper suggest the importance of US treasury to sovereign CDS market in measuring market's reference and searching for mispriced chance.In addition, a spuriously controversy result are found as rating-specific CDS benchmark rates are contrasted. A monotonic decrease of these benchmarks is clearly observed for the sovereigns with lower credit rating and higher default risk. The phenomenon is carefully explained and the main reason comes from the higher CDS rate than yield spread. This invites a further comparison of the price discovery processes in sovereign CDS market and the corresponding sovereign bond market.

Reexamination of inflation in noncommutative space-time after Planck results

An inflationary model in the framework of noncommutative space-time may generate a nontrivial running of the scalar spectral index, but usually induces a large tensor-to-scalar ratio simultaneously. With the latest observational data from the Planck mission, we reexamine the inflationary scenarios in a noncommutative space-time. We find that either the running of the spectral index is tiny compared with the recent observational result, or the tensor-to-scalar ratio is too large to allow a sufficient number of $e$-folds. As examples, we show that the chaotic and power-law inflation models with the noncommutative effects are not favored by the current Planck data.Comment: 8 pages, 4 figures; version published in Physical Review