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Some Orbits of Free Words that are Determined by Measures on Finite Groups
Liam Hanany, Chen Meiri, Doron Puder
Every word in a free group induces a probability measure on every finite group in a natural manner. It is an open problem whether two words that induce the same measure on ever…
Automorphism-invariant positive definite functions on free groups
Benoît Collins, Michael Magee, Doron Puder
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 intende…
Matrix Group Integrals, Surfaces, and Mapping Class Groups II: and
Michael Magee, Doron Puder
Let be a word in the free group on generators. The expected value of the trace of the word in independent Haar elements of gives a function ${\cal T}r_{…
Surface Words are Determined by Word Measures on Groups
Michael Magee, Doron Puder
Every word in a free group naturally induces a probability measure on every compact group . For example, if is the commutator word, a random element sam…