Convergence to closed-form distribution for the backward $SL{E}_{\kappa }$ at some random times and the phase transition at $\kappa =8$

Terry J. Lyons, Vlad Margarint, Sina Nejad

We study a one-dimensional SDE that we obtain by performing a random time change of the backward Loewner dynamics in $\mathbb{H}$. The stationary measure for this SDE has a closed-…