# 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

An invariance principle for ergodic scale-free random environments
E Gwynne, J Miller, S Sheffield
– Acta Mathematica
(2022)
228,
303
Liouville quantum gravity and the Brownian map II: Geodesics and continuity of the embedding
J Miller, S Sheffield
– The 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
Conformal covariance of the Liouville quantum gravity metric for γ∈(0,2)
E Gwynne, J Miller
– Annales de l'Institut Henri Poincaré, Probabilités et Statistiques
(2021)
57,
1016
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,
1097
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
An axiomatic characterization of the Brownian map
J Miller, S Sheffield
– Journal de l'Ecole Polytechnique - Mathematiques
(2021)
8,
609
Liouville quantum gravity as a mating of trees
B Duplantier, J Miller, S Sheffield
– Asterisque
(2021)
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