1,301 research outputs found
Coalescence of Euclidean geodesics on the Poisson-Delaunay triangulation
Let us consider Euclidean first-passage percolation on the Poisson-Delaunay
triangulation. We prove almost sure coalescence of any two semi-infinite
geodesics with the same asymptotic direction. The proof is based on an adapted
Burton-Keane argument and makes use of the concentration property for
shortest-path lengths in the considered graphs. Moreover, by considering the
specific example of the relative neighborhood graph, we illustrate that our
approach extends to further well-known graphs in computational geometry. As an
application, we show that the expected number of semi-infinite geodesics
starting at a given vertex and leaving a disk of a certain radius grows at most
sublinearly in the radius.Comment: 21 pages, 7 figure
Large deviations for the capacity in dynamic spatial relay networks
We derive a large deviation principle for the space-time evolution of users
in a relay network that are unable to connect due to capacity constraints. The
users are distributed according to a Poisson point process with increasing
intensity in a bounded domain, whereas the relays are positioned
deterministically with given limiting density. The preceding work on capacity
for relay networks by the authors describes the highly simplified setting where
users can only enter but not leave the system. In the present manuscript we
study the more realistic situation where users leave the system after a random
transmission time. For this we extend the point process techniques developed in
the preceding work thereby showing that they are not limited to settings with
strong monotonicity properties.Comment: 24 pages, 1 figur
The economics of rating watchlists: evidence from rating changes
Generally, information provision and certification have been identified as the major economic functions of rating agencies. This paper analyzes whether the “watchlist" (rating review) instrument has extended the agencies' role towards a monitoring position, as proposed by Boot, Milbourn, and Schmeits (2006). Using a data set of Moody's rating history between 1982 and 2004, we find that the overall information content of rating action has indeed increased since the introduction of the watchlist procedure. Our findings suggest that rating reviews help to establish implicit monitoring contracts between agencies and borrowers and as such enable a finer partition of rating information, thereby contributing to a higher information quality
Continuum percolation for Cox point processes
We investigate continuum percolation for Cox point processes, that is,
Poisson point processes driven by random intensity measures. First, we derive
sufficient conditions for the existence of non-trivial sub- and super-critical
percolation regimes based on the notion of stabilization. Second, we give
asymptotic expressions for the percolation probability in large-radius,
high-density and coupled regimes. In some regimes, we find universality,
whereas in others, a sensitive dependence on the underlying random intensity
measure survives.Comment: 21 pages, 5 figure
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