Cutoff for the Brownian Motion on the Unitary Quantum Group

Abstract: We introduce an analog of the Brownian motion on free unitary quantum groups UN+​. We will discuss the construction of this Brownian motion, computing its cutoff, where convergence to equilibrium undergoes a sharp transition. We will also examine the cutoff profile, analyzing the fine-scale behavior of the total variation distance around the cutoff. Unlike classical or orthogonal quantum groups, the study of UN+​ has additional challenges, such as non-absolute continuity, distinct properties of its central algebra and inabilities to clearly identify a Brownian motion.

operator algebrasquantum algebra

Audience: researchers in the topic

Quantum Groups Seminar [QGS]

Series comments: This online seminar aims to bring together experts in the area of quantum groups. The seminar topics will cover the theory of quantum groups and related structures in a large sense: Hopf algebras, operator algebras, q-deformations, higher categories and related branches of noncommutative mathematics.

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