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Tightness of Liouville first passage percolation for γ ∈ ( 0 , 2 ) $\gamma \in (0,2)$
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…
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Asymptotic analysis of downlink MISO systems over Rician fading channels
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…
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Weak LQG metrics and Liouville first passage percolation
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…
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Liouville metric of star-scale invariant fields: tails and Weyl scaling
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…
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Volume of metric balls in Liouville quantum gravity
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…
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A renormalization approach to the Liouville quantum gravity metric
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Metric growth dynamics in Liouville quantum gravity
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,…
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Liouville quantum gravity from random matrix dynamics
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…
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