A L\'evy-Khinchin formula for free groups
Uffe Haagerup, S{\o}ren Knudby
TL;DR
This paper derives a Lévy-Khinchin formula for radial functions on free groups, providing a new analytical tool and establishing bounds on the growth of certain negative definite functions.
Contribution
It introduces a Lévy-Khinchin formula tailored for free groups and applies it to bound the growth of radial, conditionally negative definite functions.
Findings
Established a Lévy-Khinchin formula for free groups
Derived linear growth bounds for negative definite functions
Enhanced understanding of harmonic analysis on free groups
Abstract
We find a L\'evy-Khinchin formula for radial functions on free groups. As a corollary we obtain a linear bound on the growth of radial, conditionally negative definite functions on free groups of two or more generators.
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