Total current fluctuations in the asymmetric simple exclusion process

Craig A. Tracy and Harold Widom

A limit theorem for the total current in the asymmetric simple exclusion process (ASEP) with step initial condition is proven. This extends the result of Johansson on TASEP to ASEP.

J. Math. Phys. 50, 095204 (2009)

A universal magnification theorem. II. Generic caustics up to codimension five

A. B. Aazami and A. O. Petters

We prove that for a generic family of general mappings between planes exhibiting singularities up to codimension five, and for a point in the target lying anywhere in the region giving rise to the maximum number of real preimages (lensed images), the total signed magnification of the preimages will always sum to zero. The wide field imaging surveys slated to be conducted by the Large Synoptic Survey Telescope are expected to find observational evidence for many of these higher-order caustic singularities.

J. Math. Phys. 50, 082501 (2009)