Electroweak Interactions: Summary

The session on precision studies of electroweak interactions is summarized. The contributions address the bilinear, trilinear, quartic as well as heavy-quark interactions of the electroweak gauge bosons. This makes up a picture of the physics of electroweak symmetry and symmetry breaking which can be investigated with the proposed design of e+e- Linear Colliders and detectors.Comment: 8 pages, no figures, uses aipproc.sty. Contribution to the Linear Collider Workshop 2000, Fermilab, October 200

Green functions for killed random walks in the Weyl chamber of Sp(4)

We consider a family of random walks killed at the boundary of the Weyl chamber of the dual of $\rm{Sp}(4)$, which in addition satisfies the following property: for any $n\geq 3$, there is in this family a walk associated with a reflection group of order $2n$. Moreover, the case $n=4$ corresponds to a process which appears naturally by studying quantum random walks on the dual of $\rm{Sp}(4)$. For all the processes belonging to this family, we find the exact asymptotic of the Green functions along all infinite paths of states as well as that of the absorption probabilities along the boundaries.Comment: 20 page

Green functions and Martin compactification for killed random walks related to SU(3)

We consider the random walks killed at the boundary of the quarter plane, with homogeneous non-zero jump probabilities to the eight nearest neighbors and drift zero in the interior, and which admit a positive harmonic polynomial of degree three. For these processes, we find the asymptotic of the Green functions along all infinite paths of states, and from this we deduce that the Martin compactification is the one-point compactification.Comment: 13 page

Counting walks in a quadrant: a unified approach via boundary value problems

The aim of this article is to introduce a unified method to obtain explicit integral representations of the trivariate generating function counting the walks with small steps which are confined to a quarter plane. For many models, this yields for the first time an explicit expression of the counting generating function. Moreover, the nature of the integrand of the integral formulations is shown to be directly dependent on the finiteness of a naturally attached group of birational transformations as well as on the sign of the covariance of the walkComment: 28 pages; 6 figure

Dressing preserving the fundamental group

In this note we consider the relationship between the dressing action and the holonomy representation in the context of constant mean curvature surfaces. We characterize dressing elements that preserve the topology of a surface and discuss dressing by simple factors as a means of adding bubbles to a class of non finite type cylinders.Comment: 36 pages, 1 figur