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papers

Publications (8)

math.PR2020

Weak LQG metrics and Liouville first passage percolation

Julien DubÃ©dat, Hugo Falconet, Ewain Gwynne +2

For $I^^{3} \in (0, 2)$ , we define a weak $I^^{3}$ -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) a…

math.PR2019

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

Julien DubÃ©dat, 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 $I^_{c}^{3} > 0$ , the left-rig…

math.PR2025

Liouville quantum gravity from random matrix dynamics

Paul Bourgade, Hugo Falconet

We establish the first connection between $2 d$ Liouville quantum gravity and natural dynamics of random matrices. In particular, we show that if $(U_{t})$ is a Brownian motion on the…

math.PR2022

Metric growth dynamics in Liouville quantum gravity

Julien DubÃ©dat, Hugo Falconet

We consider the metric growth in Liouville quantum gravity (LQG) for $I^^{3} \in (0, 2)$ . We show that a process associated with the trace of the free field on the boundary of a filled L…

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 $I^^{3} \in (0, 2)$ , it has been known since the early work of Kahane (1985) and Molchan (1996) that the LQG v…

cs.IT2016

Asymptotic analysis of downlink MIMO systems over Rician fading channels

Hugo Falconet, Luca Sanguinetti, Abla Kammoun +1

In this work, we focus on the ergodic sum rate in the downlink of a single-cell large-scale multi-user MIMO system in which the base station employs N antennas to communicate with…

math.PR2022

Random clusters in the Villain and XY models

In the Ising and Potts model, random cluster representations provide a geometric interpretation to spin correlations. We discuss similar constructions for the Villain and XY models…

math.PR2020

Tightness of Liouville first passage percolation for $I^^{3} \in (0, 2)$

We study Liouville first passage percolation metrics associated to a Gaussian free field $h$ mollified by the two-dimensional heat kernel $p_{t}$ in the bulk, and related star-scale…

Publications (8)

Weak LQG metrics and Liouville first passage percolation

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

Liouville quantum gravity from random matrix dynamics

Metric growth dynamics in Liouville quantum gravity

Volume of metric balls in Liouville quantum gravity

Asymptotic analysis of downlink MIMO systems over Rician fading channels

Random clusters in the Villain and XY models

Tightness of Liouville first passage percolation for I^3∈(0,2)

Tightness of Liouville first passage percolation for $I^^{3} \in (0, 2)$