Automorphism-invariant positive definite functions on free groups

Abstract

In this article we raise some new questions about positive definite functions on free groups, and explain how these are related to more well-known questions. The article is intended as a survey of known results that also offers some new perspectives and interesting observations; therefore the style is expository.

arXiv comment24 pages

References in corpus (7)

• Integration with respect to the Haar measure on unitary, orthogonal and symplectic group
• Second Order Freeness and Fluctuations of Random Matrices: II. Unitary Random Matrices
• Measure Preserving Words are Primitive
• Combinatorial aspects of Connes's embedding conjecture and asymptotic distribution of traces of products of unitaries
• Matrix Group Integrals, Surfaces, and Mapping Class Groups I: $U(n)$
• Some Orbits of Free Words that are Determined by Measures on Finite Groups
• Surface Words are Determined by Word Measures on Groups

Cited by in corpus (2)

• Word Measures on Symmetric Groups
• Random Unitary Representations of Surface Groups I: Asymptotic expansions