On the Naruse hook length formula and mixing times

par Lucas Teyssier (IECL)

jeudi 30 avr. 2026, 14:00 → 15:00 Europe/Paris

Fokko du Cloux (ICJ)

In 2014, Naruse discovered a generalization of the hook-length formula, which enables computing the number of standard Young tableaux of a skew Young diagram. Using this formula, we established optimal asymptotic bounds on the characters of symmetric groups, which are also the eigenvalues of conjugacy invariant random walks on symmetric groups; and derived optimal estimates of the mixing times for these walks (L^2 bounds and limiting profiles).

The first half of the talk will be devoted to presenting the Naruse hook-length formula. The second will explain how to use this formula some consequences of these bounds for mixing times. The talk mainly focuses on Sections 2 and 3 of the article https://arxiv.org/pdf/2503.12735.