The many-to-few lemma and multiple spines

2011/06/23 by Harris, Simon C., Roberts, Matthew I. · 8 citations
#60J80 #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.1106.4761

Abstract

We develop a simple and intuitive identity for calculating expectations of weighted k-fold sums over particles in branching processes, generalising the well-known many-to-one lemma.

Cited by

• Precise cover times for branching random walks on Hamming graphs: (iterated) logarithmic corrections
• From multitype branching Brownian motions to branching Markov additive processes
• A simpler path to Ergodic Theorems for the Frontier of Branching Brownian Motion
• Scaling limits for the critical level-set percolation of the Gaussian free field on regular trees
• Hyperbolic branching Brownian motion: the empirical limit measure
• Moments of density-dependent branching processes and their genealogy
• A shape theorem for BBM in a periodic environment
• Large Deviations of First Passage Times of Branching Random Walks in ℝ^d: Asymptotics and Algorithms

Related

• A strong law of large numbers for branching processes: almost sure spine\n events
• Catalytic branching processes via spine techniques and renewal theory
• Many-to-few for non-local branching Markov process
• A new formulation of the spine approach to branching diffusions
• Convergence of weighted branching processes