  In this article, we study multiple $SLE_\kappa$, for $\kappa\in(0,4]$, driven
by Dyson Brownian motion. This model was introduced in the unit disk by Cardy
in connection with the Calogero-Sutherland model. We prove the Carath\'eodory
convergence of perturbed Loewner chains under different initial conditions and
under different diffusivity $\kappa \in (0,4]$ for the case of $N=2$ driving
forces. Our proofs use the analysis of Bessel processes and estimates on
Loewner differential equation with multiple driving forces. In the last
section, we estimate the Hausdorff distance of the hulls under perturbations of
the driving forces, with assumptions on the modulus of the derivative of the
multiple Loewner maps.
