no. 5
On the norms of the random walks on planar graphs
Annales de l'Institut Fourier, Tome 47 (1997) no. 5, pp. 1463-1490.

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.

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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. https://aif.centre-mersenne.org/articles/10.5802/aif.1606/

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