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Regular variation and free regular infinitely divisible laws

Author

Listed:
  • Chakrabarty, Arijit
  • Chakraborty, Sukrit
  • Hazra, Rajat Subhra

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.

Suggested Citation

  • Chakrabarty, Arijit & Chakraborty, Sukrit & Hazra, Rajat Subhra, 2020. "Regular variation and free regular infinitely divisible laws," Statistics & Probability Letters, Elsevier, vol. 156(C).
    • Handle: RePEc:eee:stapro:v:156:y:2020:i:c:s0167715219302536
    DOI: 10.1016/j.spl.2019.108607
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