Characterisation of Planar Brownian Multiplicative Chaos

Abstract We characterise the multiplicative chaos measure $${\mathcal {M}}$$ M associated to planar Brownian motion introduced in Bass et al. (Ann Probab 22(2):566–625, 1994), Aïdékon (Ann. Probab. 48(4), 1785–1825, 2020) and Jego 48(4):1597–1643, by showing that it is only random Borel satisfying a list of natural properties. These properties serve fix average value express spatial Markov property. As consequence our characterisation, we establish scaling limit set thick points simple walk, stopped at first exit time domain, weak convergence towards point points. In particular, obtain appropriately normalised number walk nondegenerate variable. The normalising constant different from Gaussian free field, as conjectured (Electron J 25:39, 2020). results cover entire subcritical regime. A key new idea for this characterisation introduce measures describing intersection between independent trajectories how they interact create