Local limit theorems for multiplicative free convolutions Academic Article uri icon


  • 2014 Elsevier Inc. This paper describes the quality of convergence to an infinitely divisible law relative to free multiplicative convolution. We show that convergence in distribution for products of identically distributed and infinitesimal free random variables implies superconvergence of their probability densities to the density of the limit law. Superconvergence to the marginal law of free multiplicative Brownian motion at a specified time is also studied. In the unitary case, the superconvergence to free Brownian motion and that to the Haar measure are shown to be uniform over the entire unit circle, implying further a free entropic limit theorem and a universality result for unitary free Lvy processes. Finally, the method of proofs on the positive half-line gives rise to a new multiplicative Boolean to free Bercovici-Pata bijection.

published proceedings


author list (cited authors)

  • Anshelevich, M., Wang, J., & Zhong, P.

citation count

  • 7

complete list of authors

  • Anshelevich, Michael||Wang, Jiun-Chau||Zhong, Ping

publication date

  • January 2014