Current mood:

nostalgic

MSR Theory Talk, $1 Challenge
Кто поможет объяснить, о чем эта завтрашняя лекция MS Research? Моих воспоминаний не хватает чтобы понять, что это.

ABSTRACT:
We construct "quantum wedges" which are, roughly speaking, random metrics of the form e^{ih(z)} dz where h is an instance of the free boundary Gaussian free field on an infinite wedge of the form {z : a < arg (z) < b}.

We show how conformally welding one side of one wedge to one side of another wedge produces a new wedge of different width --- and "conformally welding" two sides of a wedge produces an analogously defined "quantum cone." We explicitly derive the formula relating old widths to new width. We also explain why, if one chooses an interior (boundary) point in Liouville gravity conditioned to be on some fractal set, the local behavior of the random metric near that point is that of a quantum cone (wedge) whose width is an (easily described) function of the quantum dimension of the fractal. Using the above facts and the KPZ formula, one can derive many Euclidean scaling exponents, such as the Brownian intersection exponents.

We also derive Markov properties of the continuum fields for various kappa values that give evidence for the conjecture that Liouville quantum gravity is the scaling limit of discrete quantum gravity