Poisson Dirichlet$(\alpha,\theta)$-Bridge Equations and Coagulation-Fragmentation Duality

TL;DR

This paper explores the mathematical duality between coagulation and fragmentation processes, focusing on Poisson-Dirichlet bridge equations, and extends existing formulas in the literature.

Contribution

It introduces new Poisson-Dirichlet bridge equations and elaborates on their role in coagulation-fragmentation duality, advancing theoretical understanding.

Findings

Derived new duality formulas for coagulation and fragmentation.

Extended existing literature with novel Poisson-Dirichlet bridge equations.

Enhanced the mathematical framework for coagulation-fragmentation processes.

Abstract

Paper discusses fragmentation coagulation duality formula related to those already appearing in the literature.