A non-technical introduction to the Liouville quantum gravity metric

Abstract: Informally speaking, the Liouville quantum gravity (LQG) metric is a random Riemannian metric on the complex plane given by the metric tensor $\exp(2\xi h) (dx^2+dy^2)$ where \xi is a parameter and h is an appropriate version of the Gaussian free field on $\mathbb{C}$. In this talk, we shall recall basic definitions and review some of the recent developments on the construction of this metric and understanding of its basic properties. I shall ignore most technical aspects and focus on geometric results that are particularly interesting from a first passage percolation perspective.

probability

Audience: advanced learners

Bangalore Probability Seminar

Series comments: The link to zoom meeting can be found on the seminar's google calendar - www.isibang.ac.in/~d.yogesh/BPS.html