Convergence towards an asymptotic shape in first-passage percolation on cone-like subgraphs of the integer lattice

In first-passage percolation on the integer lattice, the Shape Theorem provides precise conditions for convergence of the set of sites reachable within a given time from the origin, once rescaled, to a compact and convex limiting shape. Here, we address convergence towards an asymptotic shape for cone-like subgraphs of the $\Z^d$ lattice, where $d\ge2$. In particular, we identify the asymptotic shapes associated to these graphs as restrictions of the asymptotic shape of the lattice. Apart from providing necessary and sufficient conditions for $L^p$- and almost sure convergence towards this shape, we investigate also stronger notions such as complete convergence and stability with respect to a dynamically evolving environment.Comment: 23 pages. Together with arXiv:1305.6260, this version replaces the old. The main results have been strengthened and an earlier error in the statement corrected. To appear in J. Theoret. Proba

Consumption processes and positively homogeneous projection properties

We constructively prove the existence of time-discrete consumption processes for stochastic money accounts that fulfill a pre-specified positively homogeneous projection property (PHPP) and let the account always be positive and exactly zero at the end. One possible example is consumption rates forming a martingale under the above restrictions. For finite spaces, it is shown that any strictly positive consumption strategy with restrictions as above possesses at least one corresponding PHPP and could be constructed from it. We also consider numeric examples under time-discrete and -continuous account processes, cases with infinite time horizons and applications to income drawdown and bonus theory.Comment: 24 pages, 2 figure

Diffractive production of high pt photons at HERA

We study the diffractive production of high pt photons at HERA. We have implemented the process as a new hard sub-process in the HERWIG event generator in order to prepare the ground for a future measurement.Comment: 4 pages, 4 figures. Contribution to the 1999 UK Phenomenology Workshop on Collider Physics, Durham, U

Archaeological Studies for the San Antonio Channel Improvement Project, including Investigations at Guenther\u27s Upper Mill (41BX342)

Under Contract No. DACW63-81-C-0022 to the Department of the Army, Corps of Engineers, Fort Worth District, the Center for Archaeological Research, The University of Texas at San Antonio, in the spring of 1981, conducted historic research and survey in the areas to be affected by the San Antonio Channel Improvement Project. In the summer of 1981, extensive archaeological testing and excavation were done to determine the extent of the structural remains on the sites of Guenther\u27s Upper Mill and the Stribling House. In the spring and summer of 1982, the Center documented the removal and replacement of the mill\u27s west wall. As a result of the investigations, it can now be affirmed that most of the foundation of the east section of the mill is still present beneath the ground. The main foundation walls are made of cut limestone and measure two feet in thickness, except for the west wall which is three feet thick. Of the other buildings at various times related to the mill, only portions of a late (ca. 1910) stone and cement foundation for the Reigler Creamery still remain in the ground. The survey revealed no other cultural resources to be affected by the project