Regular variation and free regular infinitely divisible laws
Statistics and Probability Letters
In this article the relation between the tail behaviours of a free regular infinitely divisible probability measure and its Lévy 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.
Chakrabarty, Arijit; Chakraborty, Sukrit; and Hazra, Rajat Subhra, "Regular variation and free regular infinitely divisible laws" (2020). Journal Articles. 547.