We describe a new class of propagation-invariant light beams with Fourier transform given by an eigenfunction of the quantum mechanical pendulum. These beams, whose spectra (restricted to a circle) are doubly periodic Mathieu functions in azimuth, depend on a field strength parameter. When the parameter is zero, pendulum beams are Bessel beams, and as the parameter approaches infinity, they res...

We study the limit of systems of interacting particles, when the number of particle becomes very large. The support of the interaction vanishes as the number of particles goes to infinity, so that the natural limit is just free transport, but no limitation is assumed about the strength of the interaction. We obtain explicit estimates for the number of particles effectively interacting and descr...

We prove the existence of a large class of asymptotically flat initial data with non-vanishing mass and angular momentum for which the metric and the extrinsic curvature have asymptotic expansions at space-like infinity in terms of powers of a radial coordinate.

There have been many results on the asymptotics of the Painlevé transcendents in recent years, but the asymptotics of the fourth Painlevé transcendent has not been studied much. In this note, we study the general fourth Painlevé equation and develop an asymptotic representation of a group of its solutions as the independent variable approaches infinity along a straight line.

The asymptotic symmetry group (ASG) at future null infinity (I+) of four-dimensional de Sitter spacetimes is defined and shown to be given by the group of three-dimensional diffeomorphisms acting on I+. Finite charges are constructed for each choice of ASG generator together with a two-surface on I+. A conservation equation is derived relating the evolution of the charges with the radiation flu...

This paper deals with some questions that have received a lot of attention since they were raised by Hejhal and Rackner in their 1992 numerical computations of Maass forms. We establish sharp upper and lower bounds for the L2-restrictions of these forms to certain curves on the modular surface. These results, together with the Lindelof Hypothesis and known subconvex L∞-bounds are applied to pro...

We show that the total number of collisions in the exchangeable coalescent process driven by the beta (1, b) measure converges in distribution to a 1-stable law, as the initial number of particles goes to infinity. The stable limit law is also shown for the total branch length of the coalescent tree. These results were known previously for the instance b = 1, which corresponds to the Bolthausen...

An improved condition to come down from infinity for exchangeable coalescent processes with simultaneous multiple collisions of ancestral lineages is provided. For non-critical coalescents this leads to an improved necessary and sufficient condition for the coalescent to come down from infinity. An analog conjecture for the full class of exchangeable coalescents is presented. New examples of cr...

We give another proof for a result of Brick ([2]) stating that the simple connectivity at infinity is a geometric property of finitely presented groups. This allows us to define the rate of vanishing of π∞ 1 for those groups which are simply connected at infinity. Further we show that this rate is linear for cocompact lattices in nilpotent and semi-simple Lie groups, and in particular for funda...