Kassel, Adrien; Kenyon, Richard; Wu, Wei
Random two-component spanning forests
Annales de l'I.H.P. Probabilités et statistiques, Tome 51 (2015) no. 4 , p. 1457-1464
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MR 3414453
doi : 10.1214/14-AIHP625
URL stable : http://www.numdam.org/item?id=AIHPB_2015__51_4_1457_0

Nous étudions la mesure uniforme sur les forêts couvrantes à deux composantes connexes d’un graphe fini et donnons des formules pour les deux premiers moments de la taille des composantes, les probabilités d’inclusion d’un ou deux sommets dans la même composante, et la probabilité qu’une arête sépare les composantes. Nous calculons la limite des ces quantités lorsque l’on considère une suite de graphes finis qui tend vers un graphe infini périodique dans d .
We study random two-component spanning forests (2SF) of finite graphs, giving formulas for the first and second moments of the sizes of the components, vertex-inclusion probabilities for one or two vertices, and the probability that an edge separates the components. We compute the limit of these quantities when the graph tends to an infinite periodic graph in d .

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