O TYM ODCINKU
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 define a new notion of curvature, called Loewner curvature, so-named because it captures key behavior of the trace curve of the Loewner equation. The Loewner curvature is defined for (nice enough) curves that begin at a marked boundary point of a Jordan domain and grow towards a second marked boundary point. We show that if this curvature is small, then the curve must remain a simple curve.
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 define a new notion of curvature, called Loewner curvature, so-named because it captures key behavior of the trace curve of the Loewner equation. The Loewner curvature is defined for (nice enough) curves that begin at a marked boundary point of a Jordan domain and grow towards a second marked boundary point. We show that if this curvature is small, then the curve must remain a simple curve.
Język angielski
Zjednoczone Królestwo
TRANSKRYPCJA 🔗
Are you the producer of this podcast?
Add a podcast transcript
Need Audio-to-Text?
Transcribe with Listen411 in Just 60 Seconds
WYSZUKAJ MINIONE ODCINKI
Wyszukaj minione odcinki Random Geometry.
INNE ODCINKI W TYM PODCASCIE
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…
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: 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…
Zastrzeżenie: Podcast i grafika osadzone na tej stronie pochodzą z Cambridge University, który jest własnością jego właściciela i nie jest powiązany ani wspierany przez Listen Notes, Inc.
EDYTUJ
Dziękujemy za pomoc w aktualizowaniu podcastowej bazy danych.
