  Cell size control and homeostasis is a major topic in cell biology yet to be
fully understood. Several growth laws like the timer, adder, and sizer were
proposed, and mathematical approaches that model cell growth and division were
developed. This study focuses on utilizing stochastic map modeling for
investigating asymmetric cell division. We establish a mapping between the
description of cell growth and division and the Ornstein-Uhlenbeck process with
dichotomous noise. We leverage this mapping to achieve analytical solutions and
derive a closed-form expression for the stable cell size distribution under
asymmetric division. To validate our findings, we conduct numerical simulations
encompassing several cell growth scenarios. Our approach allows us to obtain a
precise criterion for a bi-phasic behavior of the cell size. While for the case
of the sizer scenario, a transition from the uni-modal phase to bi-modal is
always possible, given sufficiently large asymmetry at the division, the
affine-linear approximation of the adder scenario invariably yields uni-modal
distribution.
