# 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

Metric gluing of Brownian and $\sqrt{8/3}$-Liouville quantum gravity surfaces
E Gwynne, J Miller
– Annals of Probability
(2019)
47,
2303
Cut-off for lamplighter chains on tori: dimension interpolation and Phase transition
A Dembo, J Ding, J Miller, Y Peres
– Probability Theory and Related Fields
(2019)
173,
605
Harmonic functions on mated-CRT maps
E Gwynne, J Miller, S Sheffield
– Electronic Journal of Probability
(2019)
24,
58
Connection probabilities for conformal loop ensembles
J Miller, W Werner
– Communications in Mathematical Physics
(2018)
362,
415
Active spanning trees with bending energy on planar maps and SLE-decorated Liouville quantum gravity for $\kappa > 8$
E Gwynne, A Kassel, J Miller, DB Wilson
– Communications in Mathematical Physics
(2018)
358,
1065
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 $\kappa>8$
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
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