1,892 research outputs found
New Results for the Two-Stage Contact Process
Here we continue the work started by Steve Krone on the two-stage contact
process. We give a simplified proof of the duality relation, and answer most of
the open questions posed in that paper. We also fill in the details of an
incomplete proof.Comment: 12 pages, 0 figure
Scaling Properties of Paths on Graphs
Let be a directed graph on finitely many vertices and edges, and assign a
positive weight to each edge on . Fix vertices and and consider the
set of paths that start at and end at , self-intersecting in any number
of places along the way. For each path, sum the weights of its edges, and then
list the path weights in increasing order. The asymptotic behaviour of this
sequence is described, in terms of the structure and type of strongly connected
components on the graph. As a special case, for a Markov chain the asymptotic
probability of paths obeys either a power law scaling or a weaker type of
scaling, depending on the structure of the transition matrix. This generalizes
previous work by Mandelbrot and others, who established asymptotic power law
scaling for special classes of Markov chains.Comment: 23 pages, 2 figure
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