Free Perpetuities I: Existence, Subordination and Tail Asymptotics

Serban Belinschi, Bartosz Kołodziejek, Kamil Szpojankowski

We study the free analogue of the classical affine fixed-point (or perpetuity) equation \[ \mathbb{X} \stackrel{d}{=} \mathbb{A}^{1/2}\mathbb{X}\,\mathbb{A}^{1/2} + \mathbb{B}, \]…