# 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

Non-simple $\SLE$ curves are not determined by their range
JP Miller, S Sheffield, W Werner
– Journal of the European Mathematical Society
(2020)
22,
669
The geodesics in Liouville quantum gravity are not Schramm–Loewner evolutions
J Miller, W Qian
– Probability Theory and Related Fields
(2019)
177,
677
Gaussian free field light cones and SLE$_\kappa(\rho)$
JP Miller, S Sheffield
– The Annals of Probability
(2019)
47,
3606
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
(2019)
374,
735
Convergence of the self-avoiding walk on random quadrangulations to SLE$_{8/3}$ on $\sqrt{8/3}$-Liouville quantum gravity
E Gwynne, J Miller
(2019)
Liouville quantum gravity spheres as matings of finite-diameter trees
JP Miller, S Sheffield
– Annales de l'Institut Henri Poincaré, Probabilités et Statistiques
(2019)
55,
1712
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)
20,
757
Metric gluing of Brownian and $\sqrt{8/3}$-Liouville quantum gravity surfaces
EN Gwynne, J Miller
– The Annals of Probability
(2019)
47,
2303
Harmonic functions on mated-CRT maps
E Gwynne, J Miller, S Sheffield
– Electronic Journal of Probability
(2019)
24,
58
Cut-off for lamplighter chains on tori: dimension interpolation and Phase transition
A Dembo, J Ding, JP Miller, Y Peres
– Probability Theory and Related Fields
(2019)
173,
605
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