Serik Sagitov: Linear-fractional branching processes with infinitely many types of particles

The linear-fractional (LF) case is a good place to start for studying various intricate issues on the behavior of Branching Processes (BP) since many calculations for the LF BPs can be done explicitly. In this talk I will first describe the simple single-type model and explain the well-known beautiful connection between the random tree formed by a LF BP and the alternating random walk tracing the contour of this tree. This construction will then be extended to the multi-type case with finitely many types bringing a new light to the earlier treatment of the LF BP with finitely many types. The main message of the talk concerns the multi-type processes with countably many types.