Geodesic
Moderate deviations for shortest-path lengths on random segment processes
Hirsch, Christian1 ; Neuhäuser, David2 ; Schmidt, Volker2
1 Weierstrass Institute for Applied Analysis and Stochastics, 10117 Berlin, Germany.
2 Institute of Stochastics, Ulm University, 89069 Ulm, Germany.
ESAIM: Probability and Statistics, Tome 20 (2016), pp. 261-292

Voir la notice de l'article provenant de la source Numdam

We consider first-passage percolation on segment processes and provide concentration results concerning moderate deviations of shortest-path lengths from a linear function in the distance of their endpoints. The proofs are based on a martingale technique developed by [H. Kesten, Ann. Appl. Probab. 3 (1993) 296–338.] for an analogous problem on the lattice. Our results are applicable to graph models from stochastic geometry. For example, they imply that the time constant in Poisson−Voronoi and Poisson−Delaunay tessellations is strictly greater than 1. Furthermore, applying the framework of Howard and Newman, our results can be used to study the geometry of geodesics in planar shortest-path trees.

Reçu le :
Accepté le :
DOI : 10.1051/ps/2016012
Classification : 60D05, 05C80, 82B43
Keywords: Random segment process, first-passage percolation, moderate deviation, shortest-path

Hirsch, Christian 1 ; Neuhäuser, David 2 ; Schmidt, Volker 2

1 Weierstrass Institute for Applied Analysis and Stochastics, 10117 Berlin, Germany.
2 Institute of Stochastics, Ulm University, 89069 Ulm, Germany. 
@article{PS_2016__20__261_0,
     author = {Hirsch, Christian and Neuh\"auser, David and Schmidt, Volker},
     title = {Moderate deviations for shortest-path lengths on random segment processes},
     journal = {ESAIM: Probability and Statistics},
     pages = {261--292},
     publisher = {EDP-Sciences},
     volume = {20},
     year = {2016},
     doi = {10.1051/ps/2016012},
     mrnumber = {3528627},
     zbl = {1384.60040},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/ps/2016012/}
}
TY  - JOUR
AU  - Hirsch, Christian
AU  - Neuhäuser, David
AU  - Schmidt, Volker
TI  - Moderate deviations for shortest-path lengths on random segment processes
JO  - ESAIM: Probability and Statistics
PY  - 2016
SP  - 261
EP  - 292
VL  - 20
PB  - EDP-Sciences
UR  - http://geodesic.mathdoc.fr/articles/10.1051/ps/2016012/
DO  - 10.1051/ps/2016012
LA  - en
ID  - PS_2016__20__261_0
ER  - 
%0 Journal Article
%A Hirsch, Christian
%A Neuhäuser, David
%A Schmidt, Volker
%T Moderate deviations for shortest-path lengths on random segment processes
%J ESAIM: Probability and Statistics
%D 2016
%P 261-292
%V 20
%I EDP-Sciences
%U http://geodesic.mathdoc.fr/articles/10.1051/ps/2016012/
%R 10.1051/ps/2016012
%G en
%F PS_2016__20__261_0
Hirsch, Christian; Neuhäuser, David; Schmidt, Volker. Moderate deviations for shortest-path lengths on random segment processes. ESAIM: Probability and Statistics, Tome 20 (2016), pp. 261-292. doi: 10.1051/ps/2016012

Cité par Sources :