# 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 conformal loop ensembles on Liouville quantum gravity and the law of CLE percolation interfaces
J Miller, S Sheffield, W Werner
– Probability Theory and Related Fields
(2021)
181,
669
Local metrics of the Gaussian free field
E Gwynne, J Miller
– Annales de l’institut Fourier
(2021)
70,
2049
Random walk on random planar maps: spectral dimension, resistance, and displacement
E Gwynne, J Miller
– Annals of Probability
(2021)
49,
Liouville quantum gravity and the Brownian map III: the conformal structure is determined
J Miller, S Sheffield
– Probability Theory and Related Fields
(2021)
179,
1183
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
– 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)
2021,
17971
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
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D2.02

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