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![Figure 1: A finite excursion h on [0,1] coding a compact real tree �h. Horizontal lines connect points of theexcursion which form equivalence classes in the tree](https://thumb-ap.123doks.com/thumbv2/123dok/979514.915662/7.612.189.428.295.431/figure-nite-excursion-horizontal-connect-theexcursion-equivalence-classes.webp)
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Moreover, the minimum (resp. maximum) number of edges for all (connected) graphs with pendent vertices and nullity η are determined, and the extremal graphs are characterized..
Moreover, the minimum (resp. maximum) number of edges for all (connected) graphs with pendent vertices and nullity η are determined, and the extremal graphs are characterized..
In the context of ran- dom permutations, this was enough to prove the existence of a coupling of partitions with the desired fragmentation property, using the fact that the
An open path in the oriented percolation is a finite alternating sequence e i , v i of edges and vertices, all of which are “open” (that is, the attached Bernoulli random variables
In an n by n complete bipartite graph with independent exponentially distributed edge costs, we ask for the minimum total cost of a set of edges of which each vertex is incident to
We prove the CLT for a random walk in a dynamical environment where the states of the environ- ment at different sites are independent Markov chains..
For example, in the case that the random rooted infinite network is just a Cayley graph (rooted, say, at the identity) with the edges marked by the generators, a positive answer to
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
