Coagulation Fragmentation Laws Induced By General Coagulations of Two-Parameter Poisson-Dirichlet Processes
| dc.creator | Ho, Man-Wai | |
| dc.creator | James, Lancelot F. | |
| dc.creator | Lau, John W. | |
| dc.date | 2006-01-25 | |
| dc.date.accessioned | 2026-07-07T06:59:17Z | |
| dc.date.available | 2026-07-07T06:59:17Z | |
| dc.description | Pitman~(1999) describes a duality relationship between fragmentation and coagulation operators. An explicit relationship is described for the two-parameter Poisson-Dirichlet laws, with parameters {\footnotesize $(α,θ)$} and $(β,θ/α)$, wherein $PD(α, θ)$ is coagulated by $PD(β,θ/α)$ for $0<α<1$, $0 \leqβ<1$ and $-β<θ/α$. This remarkable explicit agreement was obtained by combinatorial methods via exchangeable partition probability functions~(EPPF). This work discusses an alternative analysis which can feasibly extend the characterizations above to more general models of $PD(α,θ)$ coagulated with some law $Q$. The analysis exploits distributional relationships between compositions of species sampling random probability measures and coagulation operators and recent work on Cauchy-Stieltjes transforms of random probability measures by Vershik, Yor and Tsilevich (2004) and James (2002). We use this to obtain explicit descriptions in the case where {\footnotesize $Q$} corresponds to a large class of power tempered Poisson Kingman models analyzed in James~(2002). That is, explicit results are obtained for models outside of the $PD(β,θ/α)$ family. | |
| dc.identifier | https://arxiv.org/abs/math/0601608 | |
| dc.identifier | http://arxiv.org/abs/math/0601608 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/107691 | |
| dc.subject | Probability | |
| dc.subject | Primary 60G57; secondary 60G07, 60E10, 05A18 | |
| dc.title | Coagulation Fragmentation Laws Induced By General Coagulations of Two-Parameter Poisson-Dirichlet Processes | |
| dc.type | text |