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 μA 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} 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}.

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

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