Total Path Length in Power-Weight Recursive Trees: Martingale Limits and Global Fluctuations

Marek Gałązka, Hanna Wdowicka

We study total path length in recursive trees with positive deterministic attachment weights. Writing $W_n={\sum }_{i=1}^n{w}_i$ and $p_n=w_n/W_n$, we obtain exact martingale-innovatio…