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Tightness of Liouville first passage percolation for
γ
∈
(
0
,
2
)
$\gamma \in (0,2)$

- Jian Ding, Julien Dub'edat, Alexander Dunlap, Hugo Falconet
- Mathematics
- 16 April 2019

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

Asymptotic analysis of downlink MISO systems over Rician fading channels

- Hugo Falconet, L. Sanguinetti, A. Kammoun, M. Debbah
- Computer ScienceIEEE International Conference on Acoustics…
- 26 January 2016

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 K single-antenna… Expand

Weak LQG metrics and Liouville first passage percolation

- Julien Dub'edat, Hugo Falconet, Ewain Gwynne, Joshua Pfeffer, Xin Sun
- MathematicsProbability Theory and Related Fields
- 1 May 2019

For $$\gamma \in (0,2)$$ γ ∈ ( 0 , 2 ) , we define a weak $$\gamma $$ γ - Liouville quantum gravity ( LQG ) metric to be a function $$h\mapsto D_h$$ h ↦ D h which takes in an instance of the planar… Expand

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

- Julien Dubédat, Hugo Falconet
- MathematicsProbability Theory and Related Fields
- 7 September 2018

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 $$\gamma _c >0$$ γ c > 0 , the left–right… Expand

Volume of metric balls in Liouville quantum gravity

- M. Ang, Hugo Falconet, Xin Sun
- Mathematics
- 30 January 2020

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

Metric growth dynamics in Liouville quantum gravity

- Julien Dub'edat, Hugo Falconet
- Mathematics
- 27 December 2021

We consider the metric growth in Liouville quantum gravity (LQG) for γ ∈ (0, 2). We show that a process associated with the trace of the free field on the boundary of a filled LQG ball is stationary,… Expand

Liouville quantum gravity from random matrix dynamics

- P. Bourgade, Hugo Falconet
- Mathematics
- 7 June 2022

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 unitary group at… Expand