3 problems

Let $(\mathcal{A}_1,E_1,E_1'),\ldots,(\mathcal{A}_k,E_k,E_k')$ be OVI $C^*$-probability spaces over $\mathcal{B}$, and let $(\mathcal{A},E)$ be their operator-valued $C^*$-free, Bo…

Suppose that $(\mathcal{M},\varphi,\varphi')$ is an infinitesimal probability space, and let … be sets that are infinitesimally monotone in $\mathcal{M}$. For each $r$, write…

Let $s_1,\dots,s_d$ be a free semicircular family, and let $p(s_1,\dots,s_d)$ be a self-adjoint polynomial in these free semicircular variables. Continuous-density conjecture. The…