5 research outputs found
Continuous first-passage percolation and continuous greedy paths model: linear growth
We study a random growth model on introduced by Deijfen. This is a
continuous first-passage percolation model. The growth occurs by means of
spherical outbursts with random radii in the infected region. We aim at finding
conditions on the distribution of the random radii to determine whether the
growth of the process is linear or not. To do so, we compare this model with a
continuous analogue of the greedy lattice paths model and transpose results in
the lattice setting to the continuous setting.Comment: 13 pages, two appendice
From Hammersley's lines to Hammersley's trees
We construct a stationary random tree, embedded in the upper half plane, with
prescribed offspring distribution and whose vertices are the atoms of a unit
Poisson point process. This process which we call Hammersley's tree process
extends the usual Hammersley's line process. Just as Hammersley's process is
related to the problem of the longest increasing subsequence, this model also
has a combinatorial interpretation: it counts the number of heaps (i.e.
increasing trees) required to store a random permutation. This problem was
initially considered by Byers et. al (2011) and Istrate and Bonchis (2015) in
the case of regular trees. We show, in particular, that the number of heaps
grows logarithmically with the size of the permutation
Continuous first-passage percolation and continuous greedy paths model: linear growth
13 pages, two appendicesWe study a random growth model on introduced by Deijfen. This is a continuous first-passage percolation model. The growth occurs by means of spherical outbursts with random radii in the infected region. We aim at finding conditions on the distribution of the random radii to determine whether the growth of the process is linear or not. To do so, we compare this model with a continuous analogue of the greedy lattice paths model and transpose results in the lattice setting to the continuous setting
Stochastic Geometry: Boolean model and random geometric graphs
International audienceThis paper collects the four contributions which were presented during the session devoted to Stochastic Geometry at the journées MAS 2014. It is focused in particular on several questions related to the transmission of information in a general sense in different random media. The underlying models include the Boolean model, simplicial complexes or geometric random graphs induced by a point process