Pemantle's min-plus binary tree

2017/09/22 by Antonio Auffinger, Auffinger, Antonio, Dylan Cable +1 · 1 citation
Mathematics · Physics and Astronomy · Economics, Econometrics and Finance · #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.1709.07849

Abstract

We consider a stochastic process that describes several particles interacting by either merging or annihilation. When two particles merge, they combine their masses; when annihilation occurs, only the particle of smallest mass survives. Particles start at the bottom of a binary tree of depth N and move towards the root. Assuming that merging or annihilation happens independently at random, we determine the limit law of the final mass of the system in the large N limit.

Citations

• Random difference equations and Renewal theory for products of random matrices

Cited by

• Hipster random walks, random series-parallel graph and random homogeneous systems

Related

• Binary branching processes with Moran type interactions
• Particle density in diffusion-limited annihilating systems
• Mean-field forest-fire models and pruning of random trees
• Annihilating branching Brownian motion
• Linear and uniform in time bound for the binary branching model with Moran type interactions