Regular variation and free regular infinitely divisible laws

Arijit Chakrabarty, Sukrit Chakraborty and Rajat Subhra Hazra

Statistics & Probability Letters, 2020, vol. 156, issue C

Abstract: 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.

Keywords: Regular variation; Free convolution; Subexponential; Free regular measure; Product of random matrices (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1016/j.spl.2019.108607

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