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First passage percolation on the Newman-Watts small world model | | Julia Komjathy
; Viktoria Vadon
; | | Date: |
25 Jun 2015 | | Abstract: | The Newman-Watts model is given by taking a cycle graph of n vertices and
then adding each possible edge $(i,j), |i-j|
eq 1 mod n$ with probability
$
ho/n$ for some $
ho>0$ constant. In this paper we add i.i.d. exponential
edge weights to this graph, and investigate typical distances in the
corresponding random metric space given by the least weight paths between
vertices. We show that typical distances grow as $frac1lambda log n$ for a
$lambda>0$ and determine the distribution of smaller order terms in terms of
limits of branching process random variables. We prove that the number of edges
along the shortest weight path follows a Central Limit Theorem, and show that
in a corresponding epidemic spread model the fraction of infected vertices
follows a deterministic curve with a random shift. | | Source: | arXiv, 1506.7693 | | Services: | Forum | Review | PDF | Favorites | |
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