Fetching the paper…
Reading the bibliography…
We prove that for any metric which one can associate with a Liouville quantum gravity (LQG) surface for $\gamma \in (0,2)$ satisfying certain natural axioms, its geodesics exhibit the following confluence property.
Tightness of Liouville first passage percolation for γ ∈ ( 0 , 2 ) \gamma\in(0,2)
J. Ding, J. Dubédat, A. Dunlap, and H. Falconet · 1904
Earlier work this paper cites.
Weak LQG metrics and Liouville first passage percolation
J. Dubédat, H. Falconet, E. Gwynne, J. Pfeffer, and X. Sun · 1905
Earlier work this paper cites.
Existence and uniqueness of the Liouville quantum gravity metric for γ ∈ ( 0 , 2 ) \gamma\in(0,2)
E. Gwynne and J. Miller · 1905
Earlier work this paper cites.
Local metrics of the Gaussian free field
E. Gwynne and J. Miller · 1905
Earlier work this paper cites.
Quantum geometry of bosonic strings
A. M. Polyakov · 1981
Earlier work this paper cites.
Positively correlated normal variables are associated
L. D. Pitt · 1982
Earlier work this paper cites.
Sur le chaos multiplicatif
J.-P. Kahane · 1985
Earlier work this paper cites.
A course in metric geometry
D. Burago, Y. Burago, and S. Ivanov · 2001
Earlier work this paper cites.
Gaussian free fields for mathematicians
S. Sheffield · 2007
Earlier work this paper cites.
Geodesics in large planar maps and in the Brownian map
J.-F. Le Gall · 2010
Cited alongside, same era.
Liouville quantum gravity and KPZ
B. Duplantier and S. Sheffield · 2011
Cited alongside, same era.
Uniqueness and universality of the Brownian map
J.-F. Le Gall · 2013
Cited alongside, same era.
The Brownian map is the scaling limit of uniform random plane quadrangulations
G. Miermont · 2013
Cited alongside, same era.
A contour line of the continuum Gaussian free field
O. Schramm and S. Sheffield · 2013
Cited alongside, same era.
Liouville quantum gravity and the Brownian map III: the conformal structure is determined
J. Miller and S. Sheffield · 2016
Later among the works it cites.
Imaginary geometry I: interacting SLEs
J. Miller and S. Sheffield · 2016
Later among the works it cites.
J. Miller and S. Sheffield · 2016
Later among the works it cites.
Compact Brownian surfaces I: Brownian disks
J. Bettinelli and G. Miermont · 2017
Later among the works it cites.
Imaginary geometry IV: interior rays, whole-plane reversibility, and space-filling trees
alphaXiv searches the wider corpus for related work and actual follow-ups.
alphaXiv is searching for related work…
R. Rhodes and V. Vargas · 2014
Cited alongside, same era.
An axiomatic characterization of the Brownian map
J. Miller and S. Sheffield · 2015
Cited alongside, same era.
Liouville quantum gravity and the Brownian map I: The QLE(8/3,0) metric
J. Miller and S. Sheffield · 2015
Cited alongside, same era.
Liouville quantum gravity and the Brownian map II: geodesics and continuity of the embedding
J. Miller and S. Sheffield · 2016
Cited alongside, same era.
J. Miller and S. Sheffield · 2017
Later among the works it cites.
The fractal dimension of Liouville quantum gravity: universality, monotonicity, and bounds
J. Ding and E. Gwynne · 2018
Later among the works it cites.
E. Gwynne, J. Miller, and S. Sheffield · 2018
Later among the works it cites.
The geodesics in Liouville quantum gravity are not Schramm-Loewner evolutions
J. Miller and W. Qian · 2018
Later among the works it cites.
KPZ formulas for the Liouville quantum gravity metric
E. Gwynne and J. Pfeffer · 2019
Closest in time.