Regular variation and free regular infinitely divisible laws
Probability
2018-10-05 v2
Abstract
In this article the relation between the tail behaviours of a free regular infinitely divisible (positively supported) probability measure and its L\'evy measure is studied. An important example of such a measure is the compound free Poisson distribution, which often occurs as a limiting spectral distribution of certain sequences of random matrices. We also describe a connection between an analogous classical result of Embrechts et al. [1979] and our result using the Bercovici-Pata bijection.
Cite
@article{arxiv.1804.07119,
title = {Regular variation and free regular infinitely divisible laws},
author = {Arijit Chakrabarty and Sukrit Chakraborty and Rajat Subhra Hazra},
journal= {arXiv preprint arXiv:1804.07119},
year = {2018}
}
Comments
Revised version, sections re-structured, new applications added and typos corrected