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Branching random walk with innite progeny mean

By Rajat Subhra Hazra

Appears in collection : Heavy Tails, Long-Range Dependence, and Beyond / Queues lourdes, dépendance de long terme et au-delà

In this talk we discuss the extremes of branching random walks under the assumption that the underlying Galton-Watson tree has in nite progeny mean. It is assumed that the displacements are either regularly varying or they have lighter tails. In the regularly varying case, it is shown that the point process sequence of normalized extremes converges to a Poisson random measure. In the lighter-tailed case, we study the asymptotics of the scaled position of the rightmost particle in the n-th generation and show the existence of a non-trivial constant. This is a joint work with Souvik Ray (Stanford), Parthanil Roy (ISI, Bangalore) and Philippe Soulier (Universite Paris Nanterre).

Information about the video

Date of recording 7/7/22
Date of publication 7/25/22
Institution CIRM
Licence CC BY NC ND
Language English
Audience Researchers, Graduate Students
Director(s) Guillaume Hennenfent
Format MP4

Citation data

DOI 10.24350/CIRM.V.19937503
Cite this video Hazra Rajat Subhra (7/7/22). Branching random walk with innite progeny mean. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.19937503
URL https://dx.doi.org/10.24350/CIRM.V.19937503

Domain(s)

Probability

Bibliography

RAY, Souvik, HAZRA, Rajat Subhra, ROY, Parthanil, et al. Branching random walk with infinite progeny mean: a tale of two tails. arXiv preprint arXiv:1909.08948, 2019. - https://doi.org/10.48550/arXiv.1909.08948

MSC codes

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