2023/01/03 by Igor Kortchemski, Paul Thévenin, Kortchemski, Igor +1
Biochemistry, Genetics and Molecular Biology · Economics, Econometrics and Finance · Mathematics · #60J80 #60J90 #Diffusion and Search Dynamics #FOS: Mathematics #Financial Risk and Volatility Modeling #Probability (math.PR) #Stochastic processes and statistical mechanics
paper · pdf · doi:10.48550/arxiv.2301.01153
openalex publication_date 2023/01/03 · openalex created_date 2023/01/06 · openalex updated_date 2026/07/28
We construct a coupling between two seemingly very different constructions of the standard additive coalescent, which describes the evolution of masses merging pairwise at rates proportional to their sums. The first construction, due to Aldous & Pitman, involves the components obtained by logging the Brownian Continuum Random Tree (CRT) by a Poissonian rain on its skeleton as time increases. The second one, due to Bertoin, involves the excursions above its running infimum of a linear-drifted standard Brownian excursion as its drift decreases. Our main tool is the use of an exploration algorithm of the so-called cut-tree of the Brownian CRT, which is a tree that encodes the genealogy of the fragmentation of the CRT.