2024/07/08 by Christopher D. Sinclair, Sinclair, Christopher D.
Computer Science · Engineering · Physics and Astronomy · #15B52 #60B05 #60B20 #60G55 #60G57 #60J80 #60K37 #82B20 #82B23 #82B31 #Adhesion, Friction, and Surface Interactions #Cellular Automata and Applications #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Probability (math.PR) #Theoretical and Computational Physics
paper · pdf · doi:10.48550/arxiv.2407.06433
openalex publication_date 2024/07/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We introduce a random probability measure on the profinite completion of the random tree of a branching process and introduce the canonical and grand canonical ensembles of random repelling particles on this random profinite completion at inverse temperature β> 0. We think of this as a random spatial process of particles in a random tree, and we introduce the notion of the \em mean canonical and grand canonical partition functions where in this context `mean' means averaged over the random environment. We give a recursion for these mean partition functions and demonstrate that in certain instances, determined by the law for the branching process, these partition functions as a function of β have algebraic properties which generalize those that appear in the non-random and p-adic environments.