Tom Hutchcroft

# Tom Hutchcroft

Email: t • hutchcroft ⓐ maths • cam • ac • uk

I am a Herchel Smith Postdoctoral Research Fellow in the Department of Pure Mathematics and Mathematical Statistics at the University of Cambridge and a Junior Research Fellow in Trinity College. Previously, I obtained my PhD in the probability group in the University of British Columbia in Vancouver under the supervision of Asaf Nachmias and Omer Angel. Before that, I completed my BA and MMath at King's College, Cambridge.

I was an intern in the Microsoft Research Theory Group in the summers of 2015, 2016, and 2017 under the mentorship of Ander Holroyd and Yuval Peres, and was supported during my PhD by Microsoft Research PhD Fellowship.

### Research interests

Probability: planar graphs, circle packing, random graphs, maps, and other structures, random walk, potential theory, spanning forests, percolation, spin systems, self-avoiding walk, probability on groups, random permutations.

### Papers

1. Non-uniqueness and mean-field criticality for percolation on nonunimodular transitive graphs. Preprint.
[ arXiv | pdf | abstract | BibTeX ]
2. Geometric and spectral properties of causal maps, with Nicolas Curien and Asaf Nachmias. Preprint.
[ arXiv | pdf | abstract | BibTeX ]
3. Counterexamples for percolation on unimodular random graphs, with Omer Angel. Preprint.
[ arXiv | pdf | abstract | BibTeX ]
4. Self-avoiding walk on nonunimodular transitive graphs. Preprint.
[ arXiv | pdf | abstract | BibTeX ]
5. The Hammersley-Welsh bound revisited. Electronic Communications in Probability, to appear.
[ arXiv | pdf | abstract | BibTeX ]
6. Finitely Dependent Cycle Coloring, with Alexander E. Holroyd and Avi Levy. Preprint.
[ arXiv | pdf | abstract | BibTeX ]
7. Harmonic Dirichlet Functions on Planar Graphs. Preprint.
[ arXiv | pdf | abstract | BibTeX ]
8. Mallows Permutations and Finite Dependence, with Alexander E. Holroyd and Avi Levy. Preprint.
[ arXiv | pdf | abstract | BibTeX ]
9. The Component Graph of the Uniform Spanning Forest: Transitions in Dimensions 9, 10, 11, ...
with Yuval Peres. Preprint.
[ arXiv | pdf | abstract | BibTeX ]
10. Hyperbolic and Parabolic Unimodular Random Maps, with Omer Angel, Asaf Nachmias
and Gourab Ray. Preprint.
[ arXiv | pdf | abstract | BibTeX ]
11. Critical percolation on any quasi-transitive graph of exponential growth has no infinite clusters. Comptes Rendus Mathematique, Volume 354, Issue 9, Pages 944-947.
[ arXiv | pdf | abstract | BibTeX ]
12. Uniform Spanning Forests of Planar Graphs. with Asaf Nachmias. Preprint.
[ arXiv | pdf | abstract | BibTeX ]
13. Interlacements and the Wired Uniform Spanning Forest. Annals of Probability, to appear.
[ arXiv | pdf | abstract | BibTeX ]
14. Boundaries of Planar Graphs: A Unified Approach. with Yuval Peres. Electronic Journal of Probability, Volume 22 (2017), paper no. 100, 20 pp.
[ arXiv | pdf | abstract | BibTeX ]
15. Indistinguishability of Trees in Uniform Spanning Forests. with Asaf Nachmias. Probability Theory and Related Fields, June 2017, Volume 168, Issue 1–2, pp 113–152.
[ arXiv | pdf | abstract | BibTeX ]
16. Collisions of Random Walks in Reversible Random Graphs. with Yuval Peres. Electronic Communications in Probability, 20, no. 63, 1-6, 2015.
[ arXiv | pdf | abstract | BibTeX ]
17. Wired Cycle-Breaking Dynamics for Uniform Spanning Forests. Annals of Probability, 44 (2016), no. 6, 3879-3892.
[ arXiv | pdf | abstract | BibTeX ]

18. Unimodular Hyperbolic Triangulations: Circle Packing and Random Walk. with Omer Angel,
Asaf Nachmias and Gourab Ray. Inventiones Mathematicae, (2016) 206: 229. doi:10.1007/s00222-016-0653-9.
[ arXiv | pdf | abstract | BibTeX ]