Statistics on monotonically ordered non-crossing partitions

Jacob Campbell (U Virginia)

Feb 20. 2025, 14:30 — 15:00

In this talk, I will introduce a new way of sampling random non-crossing partitions which takes into account their nesting structure. Specifically, the weight of a non-crossing partition corresponds to the number of its so-called monotonic orderings; this structure has appeared in the literature on monotone cumulants, and is somewhat analogous to the well-known branching structure of Young diagrams. Then, I will show how various statistics on non-crossing partitions, pairings, and related combinatorial objects behave asymptotically with respect to this new probability measure. Based on joint work with Natasha Blitvic, Thomas Bray, and Alexandru Nica.

Further Information
Venue:
ESI Boltzmann Lecture Hall
Recordings:
Recording
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)