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In § 3, we prove the main results of the present paper, namely, an unramified version of the theorem of Rumely and Moret-Bailly in positive characteristic (3.1), and an unramified
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
In this paper we shall derive asymptotic expansions of the Green function and the transition probabilities of Markov additive (MA) processes ( ξ n , S n ) whose first
If the fragmentation is inhomogeneous in time, we must also check that, for all s > t ≥ 0, the probability measure q t,s ]0 , 1[ on U governing the transition probabilities of U
We first give a strong limit law for the empirical degree distribution, and then have a closer look at the temporal evolution of the degrees of individual vertices, which we describe
The main result of this paper is the following local limit theorem for the joint distribution of the vector ( |C1| ,. , |C k | ) in the Erd˝ os-Rényi random graph:.. Theorem 1.1
The main step in the proof of Theorem 1 (ii) will be Theorem 10 below, which states that within a cube of appropriate size, the final configuration of the model resembles
Although the result in [Bourgain et al., 1992] is stated in terms of influences and not in terms of threshold phenom- ena, the proof can be rephrased and slightly adapted to show
