Non-crossing Linked Partitions and infinitesimal free multiplicative convolution

Pei-Lun Tseng (NYU, Abu Dhabi)

Feb 18. 2025, 12:00 — 12:30

Free probability theory was introduced by D. Voiculescu in the 1980s. The notion of free independence, an analogue of classical independence, provides a powerful tool for studying random matrix theory. The S-transform is one of the main tools used to analyze the distribution of the product of freely independent random variables, which is known as free multiplicative convolution.

In 2007, K. J. Dykema introduced the concept of non-crossing linked partitions, which provides a recurrence formula for computing the coefficients of the inverse of the S-transform.

In this talk, we will first briefly review this background. Then, we will introduce the concept of infinitesimal freeness, a generalization of free probability, and discuss how Dykema’s results can be extended to the infinitesimal setting.

Further Information
Venue:
ESI Boltzmann Lecture Hall
Recordings:
Recording
Files:
Slides
Associated Event:
Recent Perspectives on Non-crossing Partitions through Algebra, Combinatorics, and Probability (Workshop)
Organizer(s):
Adrian Celestino Rodriguez (TU Graz)
Kurusch Ebrahimi-Fard (NTNU, Trondheim)
James Mingo (Queen's U, Kingston)
Martin Rubey (TU Vienna)
Eleni Tzanaki (U of Crete)
Yannic Vargas (CUNEF U, Madrid)