I am a researcher in pure mathematics with interests in probability theory, and related fields. The questions I like to think about often have links with (mathematical) physics. Most of my work focuses on problems involving critical phenomena.
Bio
I moved to Cambridge in Summer 2025.
I am also Visiting Professor at Imperial College London, where I advise Wen Zhang.
A brief CV is available here.
Research
Some recent events
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Random Walks, Percolation and Mixing Time9-13 June 2025, ICMS, Edinburgh
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Geometry of Random Fields and Random Walk Clusters: New HorizonsOberwolfach Mini-Workshop, Germany, Dec 8-13, 2024
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Random Walks, Scaling Limits and CriticalityHerrsching am Ammersee, Germany, May 20-24, 2024.
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CUWB Probability-on-Sea, Playa del Carmen, MEX, Jan 8-12, 2024
Publications
Below are all my published articles and preprints, listed in reverse chronological order (by first appearance on arXiv).
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arXiv preprint (2025)
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arXiv preprint (2025)
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arXiv preprint (2023)
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arXiv preprint (2025)
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arXiv preprint (2025)
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arXiv preprint (2024)
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arXiv preprint (2024)
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Duke Mathematical Journal 172 (2023), no. 5, 839–913
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arXiv preprint (2024)
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Probability Theory and Related Fields 192, 625–720 (2025)
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arXiv preprint (2024)
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arXiv preprint (2022)
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arXiv preprint (2023)
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Annals of Probability 52, 1360–1398 (2024)
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Annals of Probability 52, 1253–1359 (2024)
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arXiv preprint (2023)
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arXiv preprint (2023)
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arXiv preprint (2023)
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[pdf] [arXiv] Existence of an unbounded nodal hypersurface for smooth Gaussian fields in dimension d ≥ 3arXiv preprint (2021)
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Inventiones Mathematicae 232, 229–299 (2023)
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Annals of Probability 50(5):1675–1724 (2022)
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Probability Theory and Related Fields 183(1-2):255–313 (2022)
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Communications in Mathematical Physics 362, 513–546 (2018)
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Journal of Functional Analysis 274(4):985–1046 (2018)
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Journal of Statistical Physics 166(3-4), 828–840 (2017)
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Probab. Theory Rel. Fields, Vol. 169, pp. 901-930 (2016).
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Electr. J. Prob., Vol. 20, pp. 1–39 (2015)
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Stoch. Proc. Appl. (SPA), Vol. 124, pp. 1469–1502 (2014)
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Comm. Math. Phys., Vol. 320, pp. 571–601 (2013)
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J. Math. Phys., Vol. 53, pp. 1–15 (2012)
A complete and up-to-date list of publications can also be found on my arXiv author page.
Teaching
In Lent 26 I will be teaching a Part III course entitled "Random Walks and Critical Phenomena". A brief course outline, including prerequisites, is available here.
From past courses:
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Lebesgue Measure and IntegrationThe lecture notes for MATH 50006 (@Imperial) are still available here.
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Stochastic ProcessesThe probabilistic construction of continuous-time Markov chains (from MATH 275C, a graduate course @UCLA).