# Department of Pure Mathematics and Mathematical Statistics

Research Interests: Schramm-Loewner evolution, Gaussian free field, Liouville quantum gravity, random planar maps, random walks, mixing times for Markov chains.

## Publications

The geodesics in Liouville quantum gravity are not Schramm-Loewner evolutions
J Miller, W Qian
– Probability Theory and Related Fields
(2019)
1
The Tutte embedding of the Poisson-Voronoi tessellation of the Brownian disk converges to $\sqrt{8/3}$-Liouville quantum gravity
E Gwynne, J Miller, S Sheffield
– Communications in Mathematical Physics
(2020)
374,
735
UNIQUENESS of the WELDING PROBLEM for SLE and LIOUVILLE QUANTUM GRAVITY
O McEnteggart, J Miller, W Qian
– Journal of the Institute of Mathematics of Jussieu
(2019)
1
Connection probabilities for conformal loop ensembles
J Miller, W Werner
– Communications in Mathematical Physics
(2018)
362,
415
Dimension of the SLE Light Cone, the SLE Fan, and ${{\rm SLE}_\kappa(\rho)}$ SLE κ ( ρ ) for ${\kappa \in (0,4)}$ κ ∈ ( 0 , 4 ) and ${\rho \in}$ ρ ∈ ${\big[{\tfrac{\kappa}{2}}-4,-2\big)}$ [ κ 2 - 4 , - 2 )
J Miller
– Communications in Mathematical Physics
(2018)
360,
1083
Brownian motion correlation in the peanosphere for $κ> 8$
E Gwynne, N Holden, J Miller, X Sun
– Annales de l Institut Henri Poincaré Probabilités et Statistiques
(2017)
53,
1866
Imaginary geometry IV: interior rays, whole-plane reversibility, and space-filling trees
J Miller, S Sheffield
– Probability Theory and Related Fields
(2017)
169,
729
Six-vertex model and Schramm-Loewner evolution
R Kenyon, J Miller, S Sheffield, DB Wilson
– Physical Review E
(2017)
95,
052146
Uniformity of the late points of random walk on ${\mathbb {Z}}_{n}^{d}$ Z n d for $d \ge 3$ d ≥ 3
J Miller, P Sousi
– Probability Theory and Related Fields
(2017)
167,
1001
CLE PERCOLATIONS
J MILLER, S SHEFFIELD, W WERNER
– Forum of Mathematics, Pi
(2017)
5,
e4
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