Sharp character bounds and cutoff for symmetric groups
read the original abstract
We develop a flexible technique to bound the characters of symmetric groups, via the Naruse hook length formula, the Larsen--Shalev character bounds, and appropriate diagram slicings. It allows us to prove a uniform exponential character bound with optimal constant $1/2$. We furthermore prove sharp character bounds for conjugacy classes having a macroscopic number of fixed points, and deduce that the random walks on the associated Cayley graphs exhibit a total variation and $L^2$ cutoff.
This paper has not been read by Pith yet.
Forward citations
Cited by 3 Pith papers
-
Cutoff profiles for conjugacy invariant random walks on symmetric groups
Proves Poissonian cutoff profiles for conjugacy-invariant random walks on symmetric groups with macroscopic fixed points and cutoff for random involution walks using character asymptotics.
-
The Cutoff Profile for Random Transpositions on Repeated Cards in the Full Range of Parameters
The cutoff profile for random transpositions on repeated cards is asymptotically Gaussian for growing multiplicity l, with explicit forms depending on whether the number of types m is fixed or grows.
-
Brownian motion on reflection quantum groups. Construction and cutoff
Constructs an analog of Brownian motion on free reflection quantum groups and computes its cutoff profile.
discussion (0)
Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.