# 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

Random walk on random planar maps: spectral dimension, resistance, and displacement
E Gwynne, J Miller
– The Annals of Probability
(2021)
49,
Existence and uniqueness of the Liouville quantum gravity metric for $\gamma \in (0,2)$
E Gwynne, J Miller
– Inventiones mathematicae
(2020)
223,
213
Confluence of geodesics in Liouville quantum gravity for $\gamma \in (0,2)$
E Gwynne, J Miller
– The Annals of Probability
(2020)
48,
1861
An almost sure KPZ relation for SLE and Brownian motion
E Gwynne, N Holden, J Miller
– The Annals of Probability
(2020)
48,
527
Conformal invariance of $\CLE_\kappa$ on the Riemann sphere for $\kappa \in (4,8)$
E Gwynne, J Miller, W Qian
– International Mathematics Research Notices
(2020)
Dimension transformation formula for conformal maps into the complement of an SLE curve
E Gwynne, N Holden, J Miller
– Probability Theory and Related Fields
(2020)
176,
649
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
Liouville quantum gravity and the Brownian map I: the $\mathrm{QLE}(8/3,0)$ metric
J Miller, S Sheffield
– Inventiones Mathematicae
(2020)
219,
75
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 $\mathrm{SLE}_{\kappa }(\rho )$
JP Miller, S Sheffield
– The Annals of Probability
(2019)
47,
3606
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