Hugo Falconet

activity

20182020

collaborators

3 papers

math.PR2020

Volume of metric balls in Liouville quantum gravity

Morris Ang, Hugo Falconet, Xin Sun

We study the volume of metric balls in Liouville quantum gravity (LQG). For $γ \in (0, 2)$ , it has been known since the early work of Kahane (1985) and Molchan (1996) that the LQG vo…

math.PR2019

Weak LQG metrics and Liouville first passage percolation

Julien Dubédat, Hugo Falconet, Ewain Gwynne +2

For $γ \in (0, 2)$ , we define a weak $γ$ -Liouville quantum gravity (LQG) metric to be a function $h \mapsto D_{h}$ which takes in an instance of the planar Gaussian free field (GFF) and…

math.PR2018

Liouville metric of star-scale invariant fields: tails and Weyl scaling

Julien Dubédat, Hugo Falconet

We study the Liouville metric associated to an approximation of a log-correlated Gaussian field with short range correlation. We show that below a parameter $γ_{c} > 0$ , the left-righ…