We show that free products of sofic groups with amalgamation over
monotileably amenable subgroups are sofic. Consequently, so are HNN extensions
of sofic groups relative to homomorphisms of monotileably amenable subgroups.
We also show that families of independent uniformly distributed permutation
matrices and certain families of non-random permutation matrices (essentially,
those coming from quasi--actions of a sofic group) are asymptotically *-free as
the matrix size grows without bound.Comment: 16 pages. Version 2 has a shorter proof of Lemma 2.2, thanks to Ion
Nechita. Version 3 corrects a mistake. The previous Lemma 3.1 was incorrect.
Version 3 has a new proof of the main result, but it is (apparently) weaker
than in Version 2. Note that the paper's title also changed accordingly.
Version 4 corrects a minor mistake around equation (4
