ОБ ЭТОМ ЭПИЗОДЕ
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 discrete curve setting, one unit of time per lattice site, and although it has not yet been shown that this discrete time parameterization converges it is still possible to define and study what should be the corresponding time parameterization for the continuum SLE curve. I will review many of the results in this direction that are due to Greg et al, along with some related results of my own in the boundary case, and then discuss some work in progress for extending the results on the boundary.
английский
объединенное Королевство
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ПОИСК ПРОШЛЫХ ЭПИЗОДОВ
Искать прошлые эпизоды Random Geometry.
ДРУГИЕ ЭПИЗОДЫ В ЭТОМ ПОДКАсте
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.
Co-author: Jean-Christophe MOURRAT (ENS Lyon)
In this talk, I will start by discussing one of Greg's many influential papers: "One-arm exponent for critical 2D percolation" by Lawler, Schramm and Werner. I will then focus on the particular case of the backbone exponent with some new insights on 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 …
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…
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