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1. CJM 2014 (vol 67 pp. 369)

Graham, Robert; Pichot, Mikael
 A Free Product Formula for the Sofic Dimension It is proved that if $G=G_1*_{G_3}G_2$ is free product of probability measure preserving $s$-regular ergodic discrete groupoids amalgamated over an amenable subgroupoid $G_3$, then the sofic dimension $s(G)$ satisfies the equality $s(G)=\mathfrak{h}(G_1^0)s(G_1)+\mathfrak{h}(G_2^0)s(G_2)-\mathfrak{h}(G_3^0)s(G_3)$ where $\mathfrak{h}$ is the normalized Haar measure on $G$. Keywords:sofic groups, dynamical systems, orbit equivalence, free entropyCategory:20E06
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