| Autor: |
Bhattacharya, Ayan, Maulik, Krishanu, Palmowski, Zbigniew, Roy, Parthanil |
| Rok vydání: |
2016 |
| Předmět: |
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| Zdroj: |
Advances in Applied Probability Vol 51 No 2, 514-540, 2019 |
| Druh dokumentu: |
Working Paper |
| DOI: |
10.1017/apr.2019.20 |
| Popis: |
We consider a branching random walk on a multi($Q$)-type, supercritical Galton-Watson tree which satisfies Kesten-Stigum condition. We assume that the displacements associated with the particles of type $Q$ have regularly varying tails of index $\alpha$, while the other types of particles have lighter tails than that of particles of type $Q$. In this article, we derive the weak limit of the sequence of point processes associated with the positions of the particles in the $n^{th}$ generation. We verify that the limiting point process is a randomly scaled scale-decorated Poisson point process (SScDPPP) using the tools developed in \cite{bhattacharya:hazra:roy:2016}. As a consequence, we shall obtain the asymptotic distribution of the position of the rightmost particle in the $n^{th}$ generation. |
| Databáze: |
arXiv |
| Externí odkaz: |
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