Séminaire Lotharingien de Combinatoire, 84B.9 (2020), 12 pp.
Hariharan Narayanan
On the Distribution of Random Words in a Compact Lie Group
Abstract.
Let G be a compact Lie group. Suppose g1,
...,
gk are chosen
independently from the Haar measure on G. Let A =
Ui in [k] Ai,
where, Ai := {gi}
union {gi-1}.
Let μAℓ be the uniform measure
over all words of length ℓ whose alphabets belong to
A. We give probabilistic bounds on the nearness of a heat kernel
smoothening of μA}ℓ to a constant function on G
in L2(G). We also give probabilistic bounds on the
maximum distance of a point in G to the support of
μA}ℓ.
Received: November 20, 2019.
Accepted: February 20, 2020.
Final version: April 30, 2020.
The following versions are available: