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)

A mathematical theory of stochastic microlensing. I. Random time delay functions and lensing maps

A. O. Petters, B. Rider, and A. M. Teguia

From first principles, we initiate the development of a mathematical theory of stochastic microlensing—a central tool in probing dark matter on galactic scales.  The results of this paper are relevant to the theory of random fields and provide a platform for further generalizations as well as analytical limits for checking astrophysical studies of stochastic microlensing.

J. Math. Phys. 50, 072503 (2009)

Variational principle for the Wheeler–Feynman electrodynamics

Jayme De Luca

We adapt the formally defined Fokker action into a variational principle for the electromagnetic-two-body problem. We introduce properly defined boundary conditions to construct a functional of a finite orbital segment into the reals. The boundary conditions for the variational principle are an end point along each trajectory plus the respective segment of trajectory for the other particle inside the light cone of each end point.

J. Math. Phys. 50, 062701 (2009)

Abstract cluster expansion with applications to statistical mechanical systems

Suren Poghosyan and Daniel Ueltschi

We formulate a general setting for the cluster expansion method and we discuss sufficient criteria for its convergence. We apply the results to systems of classical and quantum particles with stable interactions.

J. Math. Phys. 50, 053509 (2009)