Strong convergence is a phenomenon that has found applications in many areas of mathematics, such as operator algebras, random minimal surfaces, random graph lifts etc. One strategy for proving strong convergence is via linearization introduced by Haagerup and Thorbjornsen (2005). This technique reduces the study of non-commutative polynomials in random matrices to that of sums of tensorized random matrices, thereby «linearizing» the polynomials. Matrix concentration inequalities are one natural tool for the study of sums of independent random matrices with arbitrary structure. In this talk, I will describe how the matrix concentration inequalities developed in a recent work with Ramon van Handel can be applied to obtain novel strong convergence results for a wide range of random matrix ensembles with relative ease.
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