Dans cet article, on va étudier les marches aléatoires sur les graphes et sur les groupes. Enfin, on trouvera une condition nécessaire et suffisante pour la récurrence des marches aléatoires sur les groupes. La condition est très similaire à celle des marches aléatoires sur Zd. La démonstration qu’on donnera est la plus courte. Cependant, on admet le théorème 4.15 de Gromov sur la relation entr...

Bearing in mind the importance of pruning as a silvicultural treatment in cork oak (Quercus suber L.) open woodland of the dehesa type, an experiment was designed to assess the effect of pruning on cork yield. This work was carried out in two ways: synchronically, comparing pruned sites with others which were either unpruned or pruned at different times, and diachronically, comparing pruned and...

We give an upper bound for the number uΓ(n) of “overlattices” in the automorphism group of a tree, containing a fixed lattice Γ with index n. For an example of Γ in the automorphism group of a 2p-regular tree whose quotient is a loop, we obtain a lower bound of the asymptotic behavior as well. Nous donnons une borne supérieure pour le nombre uΓ(n) de “surréseaux” contenant un réseau fixé d’indi...

Let X be a locally finite tree, and let G = Aut(X). Then G is a locally compact group. In analogy with Lie groups, Bass and Lubotzky conjectured that G contains lattices, that is, discrete subgroups whose quotient carries a finite invariant measure. Bass and Kulkarni showed that G contains uniform lattices if and only if G is unimodular and G\X is finite. We describe the necessary and sufficien...

We give a deterministic algorithm to construct a graph with no loops (a tree or a forest) whose vertices are the points of a d-dimensional stationary Poisson process S ⊂Rd . The algorithm is independent of the origin of coordinates. We show that (1) the graph has one topological end – that is, from any point there is exactly one infinite self-avoiding path; (2) the graph has a unique connected ...