# Faculty of Mathematics

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

## Publications

Liouville quantum gravity and the Brownian map II: Geodesics and continuity of the embedding
J Miller, S Sheffield
– Annals of Probability
(2021)
49,
2732
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
– The Annals of Probability
(2021)
49,
Convergence of the self-avoiding walk on random quadrangulations to SLE$_{8/3}$ on $\sqrt{8/3}$-Liouville quantum gravity
E Gwynne, J Miller
– Annales Scientifiques de l École Normale Supérieure
(2021)
54,
305
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
– 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
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## Research Groups

Probability
Applied Probability
Mathematical Finance and Operational Research
Statistical Laboratory

D2.02

01223 337951