6 papers · 1 filter
On the structure of graph product von Neumann algebras
Ian Charlesworth, Rolando de Santiago, Ben Hayes +3
We undertake a comprehensive study of structural properties of graph products of von Neumann algebras equipped with faithful, normal states, as well as properties of the graph prod…
Random permutation matrix models for graph products
Ian Charlesworth, Rolando de Santiago, Ben Hayes +3
Graph independence (also known as -independence or -independence) is a mixture of classical independence and free independence corresponding to graph products or groups and o…
Strong 1-boundedness, -Betti numbers, algebraic soficity, and graph products
Ian Charlesworth, Rolando de Santiago, Ben Hayes +3
We show that graph products of non trivial finite dimensional von Neumann algebras are strongly 1-bounded when the underlying *-algebra has vanishing first L2-Betti number. The pro…
On Free Stein Dimension
Ian Charlesworth, Brent Nelson
We establish several properties of the free Stein dimension, an invariant for finitely generated unital tracial -algebras. We give formulas for its behaviour under direct sums a…
Matrix models for -free independence
Ian Charlesworth, Benoît Collins
We investigate tensor products of random matrices, and show that independence of entries leads asymptotically to -free independence, a mixture of classical and free in…
Free Stein Irregularity and Dimension
Ian Charlesworth, Brent Nelson
We introduce a free probabilistic quantity called free Stein irregularity, which is defined in terms of free Stein discrepancies. It turns out that this quantity is related via a s…