SLE Quantum Multifractality

I will present a few self-interacting random-walk-type models that somehow sit in between internal diffusion-limited aggregation and reinforced walks, associated to a strategy for proving a shape theorem for once-reinforced RW; and I will show some results in that direction.

Among Greg's many important contributions to the Schramm-Loewner evolution, he and his co-authors have in recent years been largely responsible for the construction and analysis of the natural time parameterization. The term ``natural'' refers to the parameterization favored by probabilists in the …

Co-author: Nikolai Makarov (Caltech) After implementing a version of radial conformal field theory in the OPE family of statistical fields generated by background charge modification of the Gaussian free field, I present an analytical and probabilistic proof of a well-known statement in physics th…

Co-author: Steffen Rohde (University of Washington) Inspired by the geometric understanding of the SLE trace, there has been interest in studying how the deterministic Loewner equation encodes geometric properties of 2-dim sets into the 1-dim data of the driving function. Working in this vein, we …