On considère la marche aléatoire simple sur les graphes planaires. Pour certaines familles de ces graphes, on donne des bornes supérieures explicites de la norme de l’opérateur de marche aléatoire en terme du nombre minimal des arêtes à chaque sommet. On démontre que pour un grand nombre de graphes planaires le rayon spectral de cette marche aléatoire est plus petit que un.
We consider the nearest neighbor random walk on planar graphs. For certain families of these graphs, we give explicit upper bounds on the norm of the random walk operator in terms of the minimal number of edges at each vertex. We show that for a wide range of planar graphs the spectral radius of the random walk is less than one.
@article{AIF_1997__47_5_1463_0,
author = {\.Zuk, Andrzej},
title = {On the norms of the random walks on planar graphs},
journal = {Annales de l'Institut Fourier},
pages = {1463--1490},
publisher = {Association des Annales de l{\textquoteright}institut Fourier},
volume = {47},
number = {5},
year = {1997},
doi = {10.5802/aif.1606},
mrnumber = {99g:60127},
zbl = {0897.60079},
language = {en},
url = {http://www.numdam.org/articles/10.5802/aif.1606/}
}
TY - JOUR AU - Żuk, Andrzej TI - On the norms of the random walks on planar graphs JO - Annales de l'Institut Fourier PY - 1997 SP - 1463 EP - 1490 VL - 47 IS - 5 PB - Association des Annales de l’institut Fourier UR - http://www.numdam.org/articles/10.5802/aif.1606/ DO - 10.5802/aif.1606 LA - en ID - AIF_1997__47_5_1463_0 ER -
%0 Journal Article %A Żuk, Andrzej %T On the norms of the random walks on planar graphs %J Annales de l'Institut Fourier %D 1997 %P 1463-1490 %V 47 %N 5 %I Association des Annales de l’institut Fourier %U http://www.numdam.org/articles/10.5802/aif.1606/ %R 10.5802/aif.1606 %G en %F AIF_1997__47_5_1463_0
Żuk, Andrzej. On the norms of the random walks on planar graphs. Annales de l'Institut Fourier, Tome 47 (1997) no. 5, pp. 1463-1490. doi : 10.5802/aif.1606. http://www.numdam.org/articles/10.5802/aif.1606/
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