Tom Hutchcroft

Tom Hutchcroft

360 Linde Hall
1201 E California Blvd
Pasadena, CA 91125
Email: t.hutchcroft@caltech.edu

I am a Professor of Mathematics at the California Institute of Technology, which I joined in fall 2021. Before coming to Caltech, I was a Senior Research Associate and 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. I obtained my PhD in 2017 from the University of British Columbia under the supervision of Asaf Nachmias and Omer Angel.

My research interests lie mostly in discrete probability, with some of my work touching on mathematical physics, group theory, ergodic theory, metric geometry and combinatorics.

I am an organizer of the Percolation Today webinar and an associate editor of the Annales de l'Institut Henri Poincaré.

I am also an organizer of the Los Angeles Probability Forum, a new monthly event for the LA probability community beginning in 2022.

My ORCiD is 0000-0003-0061-593X. Click here for my CV.


Teaching

Math 191c: Random walks and uniform spanning trees. Graduate topics course. Caltech, Spring 2022. Tuesdays and Thursdays 10:30-11:55am, 289 Linde Hall. 📚 Notes

Past Teaching

Random walks and uniform spanning trees. Part III graduate course. Sixteen lectures.
Cambridge, 2020. 📚 Notes 📝 Example Sheet 1 📝 Example Sheet 2 📝 Example Sheet 3

Percolation on nonamenable groups, old and new. Graduate mini-course. Four lectures.
Probabilistic Methods in Negative Curvature, ICTS Bangalore, 2021. 🎬 Video 📚 Notes

Uniform spanning forests in high dimension. Graduate mini-course. Three lectures.
Online Open Probability School, 2020. 🎬 Video 📚 Notes


Selected Online Talks

🎬 Phase transitions in hyperbolic space, Courant Institute 2020.
🎬 Power law bounds for critical long range percolation, UBC 2020.
🎬 Continuity of the Ising phase transition on nonamenable graphs, Percolation Today 2020.
🎬 Interlacements and the uniform spanning forest, CIRM 2017.
🎬 Percolation on nonunimodular graphs, Tel Aviv 2017.
🎬 The Strange Geometry of High-Dimensional Spanning Forests, MSR 2016.
🎬 Indistinguishability of Trees in Uniform Spanning Forests, Banff 2015.
🎬 Reversible Hyperbolic Triangulations: Circle Packing and Random Walk, Banff 2014.

Selected Talks by Coauthors

🎬 Perla Sousi: The uniform spanning tree in 4 dimensions, Oxford 2021.
🎬 Gabor Pete: Kazhdan groups have cost 1, Jerusalem 2018.
🎬 Nicolas Curien: Geometric and spectral properties of causal maps, Tel Aviv 2017.
🎬 Omer Angel: Parabolic and Hyperbolic Unimodular Maps, INI 2015.
🎬 Asaf Nachmias: Uniform Spanning Forests of Planar Graphs, INI 2015.


Publications & Preprints

Papers are listed in reverse chronological order by appearance on the arXiv.

Undergraduate coauthors are highlighted with a *.

See also publication lists on: The arXiv, MathSciNet, and Google Scholar.

First appeared 2022

🖥 Most transient random walks have infinitely many cut times
👥 N. Halberstam and T. Hutchcroft
📖 Preprint

🖥 Sharp hierarchical upper bounds on the critical two-point function for long-range percolation on Zd
👤 T. Hutchcroft
📖 Preprint
🎬 Percolation Today

First appeared 2021

🖥 Supercritical percolation on finite transitive graphs I: Uniqueness of the giant component
👥 P. Easo and T. Hutchcroft
📖 Preprint
🎬 Stanford | Percolation Today

🖥 The bunkbed conjecture holds in the p ↑ 1 limit
👥 T. Hutchcroft, A. Kent*, and P. Nizić-Nikolac*
📖 Preprint

🖥 High-dimensional near-critical percolation and the torus plateau
👥 T. Hutchcroft, E. Michta, and G. Slade
📖 Preprint
🎬 Percolation Today

🖥 What are the limits of universality?
👥 N. Halberstam and T. Hutchcroft
📖 Proceedings of the Royal Society Series A, 2022
🎬 Percolation Today

🖥 On the derivation of mean-field percolation critical exponents from the triangle condition
👤 T. Hutchcroft
📖 Preprint
🎬 MSRI

🖥 Non-triviality of the phase transition for percolation on finite transitive graphs
👥 T. Hutchcroft and M. Tointon
📖 Preprint
🎬 Percolation Today

🖥 The critical two-point function for long-range percolation on the hierarchical lattice
👤 T. Hutchcroft
📖 Preprint
🎬 Percolation Today

First appeared 2020

🖥 Transience and recurrence of sets for branching random walk via non-standard stochastic orders
👤 T. Hutchcroft
📖 Annales de l'Institut Henri Poincaré, to appear

🖥 Logarithmic corrections to scaling in the four-dimensional uniform spanning tree
👥 T. Hutchcroft and P. Sousi
📖 Preprint
🎬 Oxford | Percolation Today | JIPS | OOPS Course

🖥 Collisions of random walks in dynamic random environments
👥 N. Halberstam and T. Hutchcroft
📖 Electronic Journal of Probability, 2022

🖥 Power-law bounds for critical long-range percolation below the upper-critical dimension
👤 T. Hutchcroft
📖 Probability Theory and Related Fields, 2021
🎬 UBC | Oxford | Random Geometry and Statistical Physics | JIPS

🖥 Continuity of the Ising phase transition on nonamenable groups
👤 T. Hutchcroft
📖 Preprint
🎬 Percolation Today

🖥 On the tail of the branching random walk local time
👥 O. Angel, T. Hutchcroft, and A. Járai
📖 Probability Theory and Related Fields, 2021

🖥 Slightly supercritical percolation on nonamenable graphs I: The distribution of finite clusters
👤 T. Hutchcroft
📖 Preprint

First appeared 2019

🖥 Non-intersection of transient branching random walks
👤 T. Hutchcroft
📖 Probability Theory and Related Fields, 2020

🖥 Large, lengthy graphs look locally like lines
👥 I. Benjamini and T. Hutchcroft
📖 Bulletin of the London Mathematical Society, 2020

🖥 Supercritical percolation on nonamenable graphs: Isoperimetry, analyticity, and exponential decay of the cluster size distribution
👥 J. Hermon and T. Hutchcroft
📖 Inventiones Mathematicae, 2020

🖥 The L2 boundedness condition in nonamenable percolation
👤 T. Hutchcroft
📖 Electronic Journal of Probability, 2020

🖥 New critical exponent inequalities for percolation and the random cluster model
👤 T. Hutchcroft
📖 Probability and Mathematical Physics, 2020

First appeared 2018

🖥 Kazhdan groups have cost 1
👥 T. Hutchcroft and G. Pete
📖 Inventiones Mathematicae, 2020
🎬 IIAS

🖥 No percolation at criticality on certain groups of intermediate growth
👥 J. Hermon and T. Hutchcroft
📖 International Mathematics Research Notices, 2019

🖥 Locality of the critical probability for transitive graphs of exponential growth
👤 T. Hutchcroft
📖 Annals of Probability, 2020

🖥 Anomalous diffusion of random walks on random planar maps
👥 E. Gwynne and T. Hutchcroft
📖 Probability Theory and Related Fields, 2020

🖥 Percolation on hyperbolic graphs
👤 T. Hutchcroft
📖 Geometric and Functional Analysis, 2019
🎬 Courant Institute

🖥 Universality of high-dimensional spanning forests and sandpiles
👤 T. Hutchcroft
📖 Probability Theory and Related Fields, 2020
🎬 OOPS Course

🖥 Coalescing random walk on unimodular graphs
👥 E. Foxall, T. Hutchcroft, and M. Junge
📖 Electronic Communications in Probability, 2018

🖥 Mallows permutations as stable matchings
👥 O. Angel, A.E. Holroyd, T. Hutchcroft, and A. Levy
📖 Canadian Journal of Mathematics, 2020

First appeared 2017

🖥 Statistical physics on a product of trees
👤 T. Hutchcroft
📖 Annales de l'Institut Henri Poincaré, 2019

🖥 Non-uniqueness and mean-field criticality for percolation on nonunimodular transitive graphs
👤 T. Hutchcroft
📖 Journal of the American Mathematical Society, 2020
🎬 Elegance in Probability

🖥 Geometric and spectral properties of causal maps
👥 N. Curien, T. Hutchcroft, and A. Nachmias
📖 Journal of the European Mathematical Society, 2020
🎬 Elegance in Probability

🖥 Counterexamples for percolation on unimodular random graphs
👥 O. Angel and T. Hutchcroft
📖 Unimodularity in Randomly Generated Graphs (AMS Special Session Proceedings), 2018

🖥 Self-avoiding walk on nonunimodular transitive graphs
👤 T. Hutchcroft
📖 Annals of Probability, 2019

🖥 The Hammersley-Welsh bound for self-avoiding walk revisited
👤 T. Hutchcroft
📖 Electronic Communications in Probability, 2018

🖥 Finitely Dependent Cycle Coloring
👥 A.E. Holroyd, T. Hutchcroft, and A. Levy
📖 Electronic Communications in Probability, 2018

🖥 Harmonic Dirichlet Functions on Planar Graphs
👤 T. Hutchcroft
📖 Discrete and Computational Geometry, 2019

🖥 Mallows Permutations and Finite Dependence
👥 A.E. Holroyd, T. Hutchcroft, and A. Levy
📖 Annals of Probability, 2020

🖥 Indistinguishability of collections of trees in the uniform spanning forest
👤 T. Hutchcroft
📖 Annales de l'Institut Henri Poincaré, 2020

🖥 The Component Graph of the Uniform Spanning Forest: Transitions in Dimensions 9, 10, 11, ...
👥 T. Hutchcroft and Y. Peres
📖 Probability Theory and Related Fields, 2019
🎬 Northwest Probability Seminar

First appeared 2016

🖥 Hyperbolic and Parabolic Unimodular Random Maps
👥 O. Angel, T. Hutchcroft, A. Nachmias, and G. Ray
📖 Geometric and Functional Analysis, 2018
🎬 Isaac Newton Institute

🖥 Critical percolation on any quasi-transitive graph of exponential growth has no infinite clusters
👤 T. Hutchcroft
📖 Comptes Rendus Mathematique, 2016
🎬 Elegance in Probability

🖥 Uniform Spanning Forests of Planar Graphs
👥 T. Hutchcroft and A. Nachmias
📖 Forum of Mathematics Sigma, 2019
🎬 Isaac Newton Institute

First appeared 2015

🖥 Interlacements and the Wired Uniform Spanning Forest
👤 T. Hutchcroft
📖 Annals of Probability, 2018
🎬 CIRM | OOPS Course

🖥 Boundaries of Planar Graphs: A Unified Approach
👥 T. Hutchcroft and Y. Peres
📖 Electronic Journal of Probability, 2017

🖥 Indistinguishability of Trees in Uniform Spanning Forests
👥 T. Hutchcroft and A. Nachmias
📖 Probability Theory and Related Fields, 2017
🎬 Banff

🖥 Collisions of Random Walks in Reversible Random Graphs
👥 T. Hutchcroft and Y. Peres
📖 Electronic Communications in Probability, 2015

🖥 Wired Cycle-Breaking Dynamics for Uniform Spanning Forests
👤 T. Hutchcroft
📖 Annals of Probability, 2016

🖥 Unimodular Hyperbolic Triangulations: Circle Packing and Random Walk
👥 O. Angel, T. Hutchcroft, A. Nachmias, and G. Ray
📖 Inventiones Mathematicae, 2016
🎬 Banff

Other Writing

🎓 Discrete Probability and the Geometry of Graphs. PhD Thesis. UBC, 2017


Awards and Honours