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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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