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by studying the Perron vector of G , it is shown that type-I-a graphs and type-I-b (resp. type-II-a).. graphs with some specified properties are not λ 1
In this paper, by investigating the Perron vector of G, we show that type-I-a graphs are not λ 1 -extremal graphs, and type-I-b (resp. type-II-a) graphs with some.. specified
In this section we prove Proposition 2.3 on the representation of the canonical Palm distribution of the historical process and we prove Theorem 3 on the properties of the
We prove an extension of the shape result of Blach`ere and Brofferio for Internal Diffusion Limited Aggregation on a wide class of Markov chains on non-amenable graphs..
In this section we define the model of random interlacements in the more general setting of transient weighted graphs and prove the characterization of the process in terms of
Proof : The only problem is to prove formula (4), that is to prove that u is the sum of its Taylor expansion with respect to λ. In the case where A is a complex Banach algebra,
In Section 6 we prove Theorem 3.2 about the convergence of the renormalization branching process to a time-homogeneous limit.. In Section 7 , we prove the statements from
To prove this theorem we extend the bounds proved in [ 2 ] for the continuous time simple random walk on (Γ , µ ) to the slightly more general random walks X and Y defined
