Tom Hutchcroft

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

About

I am the Gordon and Betty Moore Professor of Mathematics at the California Institute of Technology.

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

Teaching

Math 2 (analytic). Fall 2024, MWF, 10:00-10:55am, Linde 310.
Course notes will be available on Canvas; see below for previous year's notes.
Past Teaching
Math 110b. Graduate course on complex analysis. 28×1 hours.
Caltech, Winter 2024.
Textbook: Basic Complex Analysis: A Comprehensive Course in Analysis, Part 2A, by Barry Simon.
Math 2 (analytic). Undergraduate course on ODEs from an analytic viewpoint. 28×1 hours.
Caltech, Fall 2022 and 2023. 📚 Notes
Math 191c: Random walks and uniform spanning trees. Graduate topics course. 18×(3/2) hours.
Caltech, Spring 2022. 📚 Notes
Random walks and uniform spanning trees. Part III graduate course. 16×1 hours.
Cambridge, 2020. 📚 Notes 📝 Example Sheet 1 📝 Example Sheet 2 📝 Example Sheet 3
Percolation on nonamenable groups, old and new. Graduate mini-course. 4×(3/2) hours.
Probabilistic Methods in Negative Curvature, ICTS Bangalore, 2021. 🎬 Video 📚 Notes
Uniform spanning forests in high dimension. Graduate mini-course. 3×1 hours.
Online Open Probability School, 2020. 🎬 Video 📚 Notes

Publications & Preprints

Papers are listed in reverse chronological order by appearance on the arXiv. Undergraduate coauthors are highlighted with an asterisk. See also lists on: The arXiv, MathSciNet, and Google Scholar.

First appeared 2025

arXiv link Critical long-range percolation I: High effective dimension
arXiv link Critical long-range percolation II: Low effective dimension
arXiv link Critical long-range percolation III: The upper critical dimension
👤 T. Hutchcroft
📖 Preprint
🎬 Hadamard Lectures | PIMS-CRM Summer School
arXiv link A fixed-point theorem for face maps, or deletion-tolerant random finite sets
👥 T. Hutchcroft, N. Monod, and O. Tamuz
📖 Preprint

First appeared 2024

arXiv link Dimension jump at the uniqueness threshold for percolation in ∞ + d dimensions
👥 T. Hutchcroft and M. Pan
📖 Preprint
arXiv link A relation between isoperimetry and total variation decay with applications to graphs of non-negative Ollivier-Ricci curvature
👥 T. Hutchcroft and I. Lopez*
📖 Preprint
arXiv link Infinite stationary measures of co-compact group actions
👥 M. Alhalimi*, T. Hutchcroft, M. Pan, O. Tamuz, and T. Zheng
📖 Preprint
arXiv link Percolation at the uniqueness threshold via subgroup relativization
👥 T. Hutchcroft and M. Pan
📖 Preprint
🎬 Percolation Today
arXiv link Small-ball estimates for random walks on groups
👤 T. Hutchcroft
📖 Preprint
arXiv link Proof of the Diaconis-Freedman Conjecture on partially-exchangeable processes
👥 N. Halberstam and T. Hutchcroft
📖 Preprint
arXiv link Pointwise two-point function estimates and a non-pertubative proof of mean-field critical behaviour for long-range percolation
👤 T. Hutchcroft
📖 Probability Theory and Related Fields, 2025

First appeared 2023

arXiv link Thick points of 4D critical branching Brownian motion
👥 N. Berestycki, T. Hutchcroft, and A. Jego
📖 Proceedings of the London Mathematical Society, to appear
🎬 Percolation Today
arXiv link The critical percolation probability is local
👥 P. Easo and T. Hutchcroft
📖 Preprint
🗞 Quanta Magazine: A Close-Up View Reveals the "Melting" Point of an Infinite Graph
🎬 Percolation Today
arXiv link Uniform finite presentation for groups of polynomial growth
👥 P. Easo and T. Hutchcroft
📖 Discrete Analysis, 2025
arXiv link Uniqueness of the infinite tree in low-dimensional random forests
👥 N. Halberstam and T. Hutchcroft
📖 Probability and Mathematical Physics, 2024
🎬 Percolation Today
arXiv link Double-exponential susceptibility growth in Dyson's hierarchical model with |x-y|-2 interaction
👥 P. Easo, T. Hutchcroft, and J. Kurrek*
📖 Journal of Mathematical Physics, 2024
arXiv link The number of ends in the uniform spanning tree for recurrent unimodular random graphs
👥 D. van Engelenburg and T. Hutchcroft
📖 Annals of Probability, 2024

First appeared 2022

arXiv link Critical cluster volumes in hierarchical percolation
👤 T. Hutchcroft
📖 Proceedings of the London Mathematical Society, 2025
🎬 Percolation Today | IAS
arXiv link Logarithmic corrections to the Alexander-Orbach conjecture for the four-dimensional uniform spanning tree
👥 N. Halberstam and T. Hutchcroft
📖 Communications in Mathematical Physics, 2024
arXiv link Transience and anchored isoperimetric dimension of supercritical percolation clusters
👤 T. Hutchcroft
📖 Electronic Journal of Probability, 2023
arXiv link Slightly supercritical percolation on nonamenable graphs II: Growth and isoperimetry of infinite clusters
👤 T. Hutchcroft
📖 Probability Theory and Related Fields, 2023.
arXiv link On the boundary at infinity for branching random walk
👥 E. Candellero and T. Hutchcroft
📖 Electronic Communications in Probability, 2023
arXiv link Most transient random walks have infinitely many cut times
👥 N. Halberstam and T. Hutchcroft
📖 Annals of Probability, 2023
arXiv link Sharp hierarchical upper bounds on the critical two-point function for long-range percolation on Zd
👤 T. Hutchcroft
📖 Journal of Mathematical Physics (Proceedings of the ICMP 2020), 2022
🏆 JMP Young Researcher Award 2023
🎬 Percolation Today

First appeared 2021

arXiv link Supercritical percolation on finite transitive graphs I: Uniqueness of the giant component
👥 P. Easo and T. Hutchcroft
📖 Duke Mathematical Journal, 2024
🎬 Stanford | Percolation Today | UT Austin
arXiv link The bunkbed conjecture holds in the p ↑ 1 limit
👥 T. Hutchcroft, A. Kent*, and P. Nizić-Nikolac*
📖 Combinatorics, Probability, and Computing, 2022
arXiv link High-dimensional near-critical percolation and the torus plateau
👥 T. Hutchcroft, E. Michta, and G. Slade
📖 Annals of Probability, 2023
🎬 Percolation Today
arXiv link What are the limits of universality?
👥 N. Halberstam and T. Hutchcroft
📖 Proceedings of the Royal Society Series A, 2022
🎬 Percolation Today
arXiv link On the derivation of mean-field percolation critical exponents from the triangle condition
👤 T. Hutchcroft
📖 Journal of Statistical Physics, 2022
🎬 MSRI
arXiv link Non-triviality of the phase transition for percolation on finite transitive graphs
👥 T. Hutchcroft and M. Tointon
📖 Journal of the European Mathematical Society, 2024
🎬 Percolation Today | UT Austin
arXiv link The critical two-point function for long-range percolation on the hierarchical lattice
👤 T. Hutchcroft
📖 Annals of Applied Probability, 2024
🎬 Percolation Today

First appeared 2020

arXiv link Transience and recurrence of sets for branching random walk via non-standard stochastic orders
👤 T. Hutchcroft
📖 Annales de l'Institut Henri Poincaré, 2022
arXiv link Logarithmic corrections to scaling in the four-dimensional uniform spanning tree
👥 T. Hutchcroft and P. Sousi
📖 Communications in Mathematical Physics, 2023
🎬 Oxford | Percolation Today | JIPS | Online Open Probability School (OOPS)
arXiv link Collisions of random walks in dynamic random environments
👥 N. Halberstam and T. Hutchcroft
📖 Electronic Journal of Probability, 2022
arXiv link 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
arXiv link Continuity of the Ising phase transition on nonamenable groups
👤 T. Hutchcroft
📖 Communications in Mathematical Physics, 2023
🎬 Percolation Today
arXiv link On the tail of the branching random walk local time
👥 O. Angel, T. Hutchcroft, and A. Járai
📖 Probability Theory and Related Fields, 2021
arXiv link Slightly supercritical percolation on nonamenable graphs I: The distribution of finite clusters
👤 T. Hutchcroft
📖 Proceedings of the London Mathematical Society, 2022

First appeared 2019

arXiv link Non-intersection of transient branching random walks
👤 T. Hutchcroft
📖 Probability Theory and Related Fields, 2020
arXiv link Large, lengthy graphs look locally like lines
👥 I. Benjamini and T. Hutchcroft
📖 Bulletin of the London Mathematical Society, 2020
arXiv link Supercritical percolation on nonamenable graphs: Isoperimetry, analyticity, and exponential decay of the cluster size distribution
👥 J. Hermon and T. Hutchcroft
📖 Inventiones Mathematicae, 2020
arXiv link The L2 boundedness condition in nonamenable percolation
👤 T. Hutchcroft
📖 Electronic Journal of Probability, 2020
arXiv link New critical exponent inequalities for percolation and the random cluster model
👤 T. Hutchcroft
📖 Probability and Mathematical Physics, 2020

First appeared 2018

arXiv link Kazhdan groups have cost 1
👥 T. Hutchcroft and G. Pete
📖 Inventiones Mathematicae, 2020
🎬 IIAS
arXiv link No percolation at criticality on certain groups of intermediate growth
👥 J. Hermon and T. Hutchcroft
📖 International Mathematics Research Notices, 2019
arXiv link Locality of the critical probability for transitive graphs of exponential growth
👤 T. Hutchcroft
📖 Annals of Probability, 2020
arXiv link Anomalous diffusion of random walks on random planar maps
👥 E. Gwynne and T. Hutchcroft
📖 Probability Theory and Related Fields, 2020
arXiv link Percolation on hyperbolic graphs
👤 T. Hutchcroft
📖 Geometric and Functional Analysis, 2019
🎬 Courant Institute
arXiv link Universality of high-dimensional spanning forests and sandpiles
👤 T. Hutchcroft
📖 Probability Theory and Related Fields, 2020
🎬 Online Open Probability School (OOPS)
arXiv link Coalescing random walk on unimodular graphs
👥 E. Foxall, T. Hutchcroft, and M. Junge
📖 Electronic Communications in Probability, 2018
arXiv link Mallows permutations as stable matchings
👥 O. Angel, A.E. Holroyd, T. Hutchcroft, and A. Levy
📖 Canadian Journal of Mathematics, 2020

First appeared 2017

arXiv link Statistical physics on a product of trees
👤 T. Hutchcroft
📖 Annales de l'Institut Henri Poincaré, 2019
arXiv link Non-uniqueness and mean-field criticality for percolation on nonunimodular transitive graphs
👤 T. Hutchcroft
📖 Journal of the American Mathematical Society, 2020
🎬 Elegance in Probability
arXiv link Geometric and spectral properties of causal maps
👥 N. Curien, T. Hutchcroft, and A. Nachmias
📖 Journal of the European Mathematical Society, 2020
🎬 Elegance in Probability
arXiv link Counterexamples for percolation on unimodular random graphs
👥 O. Angel and T. Hutchcroft
📖 Unimodularity in Randomly Generated Graphs (AMS Special Session Proceedings), 2018
arXiv link Self-avoiding walk on nonunimodular transitive graphs
👤 T. Hutchcroft
📖 Annals of Probability, 2019
arXiv link The Hammersley-Welsh bound for self-avoiding walk revisited
👤 T. Hutchcroft
📖 Electronic Communications in Probability, 2018
arXiv link Finitely Dependent Cycle Coloring
👥 A.E. Holroyd, T. Hutchcroft, and A. Levy
📖 Electronic Communications in Probability, 2018
arXiv link Harmonic Dirichlet Functions on Planar Graphs
👤 T. Hutchcroft
📖 Discrete and Computational Geometry, 2019
arXiv link Mallows Permutations and Finite Dependence
👥 A.E. Holroyd, T. Hutchcroft, and A. Levy
📖 Annals of Probability, 2020
arXiv link Indistinguishability of collections of trees in the uniform spanning forest
👤 T. Hutchcroft
📖 Annales de l'Institut Henri Poincaré, 2020
arXiv link 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

arXiv link Hyperbolic and Parabolic Unimodular Random Maps
👥 O. Angel, T. Hutchcroft, A. Nachmias, and G. Ray
📖 Geometric and Functional Analysis, 2018
🎬 Isaac Newton Institute
arXiv link Critical percolation on any quasi-transitive graph of exponential growth has no infinite clusters
👤 T. Hutchcroft
📖 Comptes Rendus Mathematique, 2016
🎬 Elegance in Probability
arXiv link Uniform Spanning Forests of Planar Graphs
👥 T. Hutchcroft and A. Nachmias
📖 Forum of Mathematics Sigma, 2019
🎬 Isaac Newton Institute

First appeared 2015

arXiv link Interlacements and the Wired Uniform Spanning Forest
👤 T. Hutchcroft
📖 Annals of Probability, 2018
🎬 CIRM | Online Open Probability School (OOPS)
arXiv link Boundaries of Planar Graphs: A Unified Approach
👥 T. Hutchcroft and Y. Peres
📖 Electronic Journal of Probability, 2017
arXiv link Indistinguishability of Trees in Uniform Spanning Forests
👥 T. Hutchcroft and A. Nachmias
📖 Probability Theory and Related Fields, 2017
🎬 Banff
arXiv link Collisions of Random Walks in Reversible Random Graphs
👥 T. Hutchcroft and Y. Peres
📖 Electronic Communications in Probability, 2015
arXiv link Wired Cycle-Breaking Dynamics for Uniform Spanning Forests
👤 T. Hutchcroft
📖 Annals of Probability, 2016
arXiv link 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

Curriculum Vitae

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.

I am an organizer of the Percolation Today webinar and an associate editor of Duke Mathematical Journal, Probability Theory and Related Fields, Probability and Mathematical Physics, and 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.

Awards and Honours