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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 *g*_{1},
...,
*g*_{k} are chosen
independently from the Haar measure on *G*. Let **A** =
U_{i in [k]} *A*_{i},
where, **A**_{i} := {*g*_{i}}
union {*g*_{i}^{-1}}.
Let μ_{A}^{ℓ} 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 μ_{A}}^{ℓ} to a constant function on *G*
in **L**^{2}(*G*). We also give probabilistic bounds on the
maximum distance of a point in *G* to the support of
μ_{A}}^{ℓ}.

Received: November 20, 2019.
Accepted: February 20, 2020.
Final version: April 30, 2020.

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