Manuscript Oai211-A@1 · Oai211-A.tex · definition · 3f3e4f63

Definition: Spine distribution

The marked tree and its spine law · lines 260–274

Oai211-A@1#def:spine, Oai211-A@1#eq:spine

The probability law of a triple $(K, I, A)$ is

P_{sp} (K = k, I = i, A \in E) = p_{k} L_{k} (E), 1 \leq i \leq k .

It is normalized because $\sum_{k} k p_{k} = 1$ . For a scalar label $b (k, i, A)$ , write

μ_{b} = E_{sp} b (K, I, A), B_{b} (v) = path (v) \sum b .

Displayed formulas in this passage

Oai211-A@1#eq:spine · line 263
$P_{sp} (K = k, I = i, A \in E) = p_{k} L_{k} (E), 1 \leq i \leq k .$
unlabeled · line 270
$μ_{b} = E_{sp} b (K, I, A), B_{b} (v) = path (v) \sum b .$