Classification of Solvable Feynman Path Integrals

A systematic classification of Feynman path integrals in quantum mechanics is presented and a table of solvable path integrals is given which reflects the progress made during the last ten years or so, including, of course, the main contributions since the invention of the path integral by Feynman in 1942. An outline of the general theory is given. Explicit formul\ae\ for the so-called basic path integrals are presented on which our general scheme to classify and calculate path integrals in quantum mechanics is based.Comment: 13 pages, amstex, preprint DESY 92--189, and SISSA/1/93/F

Gaining analytic control of parton showers

Parton showers are widely used to generate fully exclusive final states needed to compare theoretical models to experimental observations. While, in general, parton showers give a good description of the experimental data, the precise functional form of the probability distribution underlying the event generation is generally not known. The reason is that realistic parton showers are required to conserve four-momentum at each vertex. In this paper we investigate in detail how four-momentum conservation is enforced in a standard parton shower and why this destroys the analytic control of the probability distribution. We show how to modify a parton shower algorithm such that it conserves four-momentum at each vertex, but for which the full analytic form of the probability distribution is known. We then comment how this analytic control can be used to match matrix element calculations with parton showers, and to estimate effects of power corrections and other uncertainties in parton showers.Comment: 12 pages, 6 figures, v2: final journal versio

An Analysis of Aggregate Lending in Japan

Aggregate bank lending has stagnated since 1990 in Japan. This observation has generated a debate on whether the supply side of the credit market had an effect on the economy in its recent slowdown. At this point, the evidence is ambiguous. The hypothesis is primarily challenged by the low level of interest rates. However, in this paper we analyse indicators that also point towards a credit crunch explanation: the development of commercial paper, as a substitute for bank lending, and survey data on the firms’ evaluation of the lending attitude of banks. We find that while aggregate lending has stagnated, there was a continued high demand for commercial paper. Using the Short-term Economic Survey of Enterprises in Japan (Tankan), we also document that small firms felt more credit constrained than larger firms until recently in Japan. This difference has been reduced, and has lost statistical significance, however, in the recent recovery since 2003. Finally, we point out that there exists a striking similarity between the recent developments in Germany and Japan in the 1990ies.

Exploiting c\mathbf{c}-Closure in Kernelization Algorithms for Graph Problems

A graph is c-closed if every pair of vertices with at least c common neighbors is adjacent. The c-closure of a graph G is the smallest number such that G is c-closed. Fox et al. [ICALP '18] defined c-closure and investigated it in the context of clique enumeration. We show that c-closure can be applied in kernelization algorithms for several classic graph problems. We show that Dominating Set admits a kernel of size k^O(c), that Induced Matching admits a kernel with O(c^7*k^8) vertices, and that Irredundant Set admits a kernel with O(c^(5/2)*k^3) vertices. Our kernelization exploits the fact that c-closed graphs have polynomially-bounded Ramsey numbers, as we show

The Abelian Sandpile Model on an Infinite Tree

We consider the standard Abelian sandpile process on the Bethe lattice. We show the existence of the thermodynamic limit for the finite volume stationary measures and the existence of a unique infinite volume Markov process exhibiting features of self-organized criticality