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Results tagged with trees
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user 53071
A tree is a connected graph without cycles, with a finite or infinite number of vertices. There are many variants of trees, according to further constraints or decorations.
1
vote
0
answers
71
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Root degree in large subcritical Galton-Watson trees
for example requiring the following limit to exist:
$$
\lim_{k \to \infty} \mathbb{P}(\xi = k) / \mathbb{P}(\xi = k+1)
$$
A related known result (see Chapter 20 in Janson's survey "Simply generated trees … , conditioned Galton–Watson trees, random allocations and condensation") is that when $\Omega_n \to \infty$ is a deterministic sequence that tends to infinity sufficiently slowly, then
$$
\lim_{n \to \ …
- 43
3
votes
1
answer
328
views
Ratio of expected diameter and height of a conditioned Galton-Watson tree
A Galton-Watson tree is the family tree of a Galton-Watson process. Let $T_n$ denote a Galton-Watson tree conditioned on total population size $n$. The time of extinction is its height $H(T_n)$ and it …
- 43