$\mathrm{\infty }$-Operads as Analytic Monads

We develop an $\mathrm{\infty }$-categorical version of the classical theory of polynomial and analytic functors, initial algebras, and free monads. Using this machinery, we provide a new model for $\mathrm{\infty }$-operads, namely $\mathrm{\infty }$-operads as analytic monads. We justify this definition by proving that the $\mathrm{\infty }$-category of analytic monads is equivalent to that of dendroidal Segal spaces, known to be equivalent to the other existing models for $\mathrm{\infty }$-operads.