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 Probability Theory and Related Fields, Probability and Mathematical Physics, and the Annales de l'Institut Henri PoincarΓ©.

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 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. 28Γ—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. 28Γ—1 hours.
Caltech, Fall 2022 and 2023. πŸ“š Notes

Math 191c: Random walks and uniform spanning trees. Graduate topics course. 18Γ—(3/2) hours.
Caltech, Spring 2022. πŸ“š Notes

Random walks and uniform spanning trees. Part III graduate course. 16Γ—1 hours.
Cambridge, 2020. πŸ“š Notes πŸ“ Example Sheet 1 πŸ“ Example Sheet 2 πŸ“ Example Sheet 3

Percolation on nonamenable groups, old and new. Graduate mini-course. 4Γ—(3/2) hours.
Probabilistic Methods in Negative Curvature, ICTS Bangalore, 2021. 🎬 Video πŸ“š Notes

Uniform spanning forests in high dimension. Graduate mini-course. 3Γ—1 hours.
Online Open Probability School, 2020. 🎬 Video πŸ“š Notes


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 2024

πŸ–₯ Dimension jump at the uniqueness threshold for percolation in ∞ + d dimensions
πŸ‘₯ T. Hutchcroft and M. Pan
πŸ“– Preprint

πŸ–₯ A relation between isoperimetry and total variation decay with applications to graphs of non-negative Ollivier-Ricci curvature
πŸ‘₯ T. Hutchcroft and I. Lopez*
πŸ“– Preprint

πŸ–₯ Infinite stationary measures of co-compact group actions
πŸ‘₯ M. Alhalimi*, T. Hutchcroft, M. Pan, O. Tamuz, and T. Zheng
πŸ“– Preprint

πŸ–₯ Percolation at the uniqueness threshold via subgroup relativization
πŸ‘₯ T. Hutchcroft and M. Pan
πŸ“– Preprint

πŸ–₯ Small-ball estimates for random walks on groups
πŸ‘€ T. Hutchcroft
πŸ“– Preprint

πŸ–₯ Proof of the Diaconis-Freedman Conjecture on partially-exchangeable processes
πŸ‘₯ N. Halberstam and T. Hutchcroft
πŸ“– Preprint

πŸ–₯ Pointwise two-point function estimates and a non-pertubative proof of mean-field critical behaviour for long-range percolation
πŸ‘€ T. Hutchcroft
πŸ“– Preprint

First appeared 2023

πŸ–₯ Thick points of 4D critical branching Brownian motion
πŸ‘₯ N. Berestycki, T. Hutchcroft, and A. Jego
πŸ“– Preprint
🎬 Percolation Today

πŸ–₯ The critical percolation probability is local
πŸ‘₯ P. Easo and T. Hutchcroft
πŸ“– Preprint
πŸ—ž Quanta Magazine: A Close-Up View Reveals the "Melting" Point of an Infinite Graph
🎬 Percolation Today

πŸ–₯ Uniform finite presentation for groups of polynomial growth
πŸ‘₯ P. Easo and T. Hutchcroft
πŸ“– Discrete Analysis, to appear.

πŸ–₯ Uniqueness of the infinite tree in low-dimensional random forests
πŸ‘₯ N. Halberstam and T. Hutchcroft
πŸ“– Probability and Mathematical Physics, to appear.
🎬 Percolation Today

πŸ–₯ Double-exponential susceptibility growth in Dyson's hierarchical model with |x-y|-2 interaction
πŸ‘₯ P. Easo, T. Hutchcroft, and J. Kurrek*
πŸ“– Journal of Mathematical Physics, 2024

πŸ–₯ The number of ends in the uniform spanning tree for recurrent unimodular random graphs
πŸ‘₯ D. van Engelenberg and T. Hutchcroft
πŸ“– Annals of Probability, 2024

First appeared 2022

πŸ–₯ Critical cluster volumes in hierarchical percolation
πŸ‘€ T. Hutchcroft
πŸ“– Proceedings of the London Mathematical Society, to appear
🎬 Percolation Today

πŸ–₯ Logarithmic corrections to the Alexander-Orbach conjecture for the four-dimensional uniform spanning tree
πŸ‘₯ N. Halberstam and T. Hutchcroft
πŸ“– Communications in Mathematical Physics, 2024

πŸ–₯ Transience and anchored isoperimetric dimension of supercritical percolation clusters
πŸ‘€ T. Hutchcroft
πŸ“– Electronic Journal of Probability, 2023

πŸ–₯ Slightly supercritical percolation on nonamenable graphs II: Growth and isoperimetry of infinite clusters
πŸ‘€ T. Hutchcroft
πŸ“– Probability Theory and Related Fields, 2023.

πŸ–₯ On the boundary at infinity for branching random walk
πŸ‘₯ E. Candellero and T. Hutchcroft
πŸ“– Electronic Communications in Probability, 2023

πŸ–₯ Most transient random walks have infinitely many cut times
πŸ‘₯ N. Halberstam and T. Hutchcroft
πŸ“– Annals of Probability, 2023

πŸ–₯ Sharp hierarchical upper bounds on the critical two-point function for long-range percolation on Zd
πŸ‘€ T. Hutchcroft
πŸ“– Journal of Mathematical Physics (Proceedings of the ICMP 2020), 2022
πŸ† JMP Young Researcher Award 2023
🎬 Percolation Today

First appeared 2021

πŸ–₯ Supercritical percolation on finite transitive graphs I: Uniqueness of the giant component
πŸ‘₯ P. Easo and T. Hutchcroft
πŸ“– Duke Mathematical Journal, 2024
🎬 Stanford | Percolation Today

πŸ–₯ The bunkbed conjecture holds in the p ↑ 1 limit
πŸ‘₯ T. Hutchcroft, A. Kent*, and P. NiziΔ‡-Nikolac*
πŸ“– Combinatorics, Probability, and Computing, 2022

πŸ–₯ High-dimensional near-critical percolation and the torus plateau
πŸ‘₯ T. Hutchcroft, E. Michta, and G. Slade
πŸ“– Annals of Probability, 2023
🎬 Percolation Today

πŸ–₯ What are the limits of universality?
πŸ‘₯ N. Halberstam and T. Hutchcroft
πŸ“– Proceedings of the Royal Society Series A, 2022
🎬 Percolation Today

πŸ–₯ On the derivation of mean-field percolation critical exponents from the triangle condition
πŸ‘€ T. Hutchcroft
πŸ“– Journal of Statistical Physics, 2022
🎬 MSRI

πŸ–₯ Non-triviality of the phase transition for percolation on finite transitive graphs
πŸ‘₯ T. Hutchcroft and M. Tointon
πŸ“– Journal of the European Mathematical Society, 2024
🎬 Percolation Today

πŸ–₯ The critical two-point function for long-range percolation on the hierarchical lattice
πŸ‘€ T. Hutchcroft
πŸ“– Annals of Applied Probability, 2024
🎬 Percolation Today

First appeared 2020

πŸ–₯ Transience and recurrence of sets for branching random walk via non-standard stochastic orders
πŸ‘€ T. Hutchcroft
πŸ“– Annales de l'Institut Henri PoincarΓ©, 2022

πŸ–₯ Logarithmic corrections to scaling in the four-dimensional uniform spanning tree
πŸ‘₯ T. Hutchcroft and P. Sousi
πŸ“– Communications in Mathematical Physics, 2023
🎬 Oxford | Percolation Today | JIPS | OOPS Course

πŸ–₯ Collisions of random walks in dynamic random environments
πŸ‘₯ N. Halberstam and T. Hutchcroft
πŸ“– Electronic Journal of Probability, 2022

πŸ–₯ Power-law bounds for critical long-range percolation below the upper-critical dimension
πŸ‘€ T. Hutchcroft
πŸ“– Probability Theory and Related Fields, 2021
🎬 UBC | Oxford | Random Geometry and Statistical Physics | JIPS

πŸ–₯ Continuity of the Ising phase transition on nonamenable groups
πŸ‘€ T. Hutchcroft
πŸ“– Communications in Mathematical Physics, 2023
🎬 Percolation Today

πŸ–₯ On the tail of the branching random walk local time
πŸ‘₯ O. Angel, T. Hutchcroft, and A. JΓ‘rai
πŸ“– Probability Theory and Related Fields, 2021

πŸ–₯ Slightly supercritical percolation on nonamenable graphs I: The distribution of finite clusters
πŸ‘€ T. Hutchcroft
πŸ“– Proceedings of the London Mathematical Society, 2022

First appeared 2019

πŸ–₯ Non-intersection of transient branching random walks
πŸ‘€ T. Hutchcroft
πŸ“– Probability Theory and Related Fields, 2020

πŸ–₯ Large, lengthy graphs look locally like lines
πŸ‘₯ I. Benjamini and T. Hutchcroft
πŸ“– Bulletin of the London Mathematical Society, 2020

πŸ–₯ Supercritical percolation on nonamenable graphs: Isoperimetry, analyticity, and exponential decay of the cluster size distribution
πŸ‘₯ J. Hermon and T. Hutchcroft
πŸ“– Inventiones Mathematicae, 2020

πŸ–₯ The L2 boundedness condition in nonamenable percolation
πŸ‘€ T. Hutchcroft
πŸ“– Electronic Journal of Probability, 2020

πŸ–₯ New critical exponent inequalities for percolation and the random cluster model
πŸ‘€ T. Hutchcroft
πŸ“– Probability and Mathematical Physics, 2020

First appeared 2018

πŸ–₯ Kazhdan groups have cost 1
πŸ‘₯ T. Hutchcroft and G. Pete
πŸ“– Inventiones Mathematicae, 2020
🎬 IIAS

πŸ–₯ No percolation at criticality on certain groups of intermediate growth
πŸ‘₯ J. Hermon and T. Hutchcroft
πŸ“– International Mathematics Research Notices, 2019

πŸ–₯ Locality of the critical probability for transitive graphs of exponential growth
πŸ‘€ T. Hutchcroft
πŸ“– Annals of Probability, 2020

πŸ–₯ Anomalous diffusion of random walks on random planar maps
πŸ‘₯ E. Gwynne and T. Hutchcroft
πŸ“– Probability Theory and Related Fields, 2020

πŸ–₯ Percolation on hyperbolic graphs
πŸ‘€ T. Hutchcroft
πŸ“– Geometric and Functional Analysis, 2019
🎬 Courant Institute

πŸ–₯ Universality of high-dimensional spanning forests and sandpiles
πŸ‘€ T. Hutchcroft
πŸ“– Probability Theory and Related Fields, 2020
🎬 OOPS Course

πŸ–₯ Coalescing random walk on unimodular graphs
πŸ‘₯ E. Foxall, T. Hutchcroft, and M. Junge
πŸ“– Electronic Communications in Probability, 2018

πŸ–₯ Mallows permutations as stable matchings
πŸ‘₯ O. Angel, A.E. Holroyd, T. Hutchcroft, and A. Levy
πŸ“– Canadian Journal of Mathematics, 2020

First appeared 2017

πŸ–₯ Statistical physics on a product of trees
πŸ‘€ T. Hutchcroft
πŸ“– Annales de l'Institut Henri PoincarΓ©, 2019

πŸ–₯ Non-uniqueness and mean-field criticality for percolation on nonunimodular transitive graphs
πŸ‘€ T. Hutchcroft
πŸ“– Journal of the American Mathematical Society, 2020
🎬 Elegance in Probability

πŸ–₯ Geometric and spectral properties of causal maps
πŸ‘₯ N. Curien, T. Hutchcroft, and A. Nachmias
πŸ“– Journal of the European Mathematical Society, 2020
🎬 Elegance in Probability

πŸ–₯ Counterexamples for percolation on unimodular random graphs
πŸ‘₯ O. Angel and T. Hutchcroft
πŸ“– Unimodularity in Randomly Generated Graphs (AMS Special Session Proceedings), 2018

πŸ–₯ Self-avoiding walk on nonunimodular transitive graphs
πŸ‘€ T. Hutchcroft
πŸ“– Annals of Probability, 2019

πŸ–₯ The Hammersley-Welsh bound for self-avoiding walk revisited
πŸ‘€ T. Hutchcroft
πŸ“– Electronic Communications in Probability, 2018

πŸ–₯ Finitely Dependent Cycle Coloring
πŸ‘₯ A.E. Holroyd, T. Hutchcroft, and A. Levy
πŸ“– Electronic Communications in Probability, 2018

πŸ–₯ Harmonic Dirichlet Functions on Planar Graphs
πŸ‘€ T. Hutchcroft
πŸ“– Discrete and Computational Geometry, 2019

πŸ–₯ Mallows Permutations and Finite Dependence
πŸ‘₯ A.E. Holroyd, T. Hutchcroft, and A. Levy
πŸ“– Annals of Probability, 2020

πŸ–₯ Indistinguishability of collections of trees in the uniform spanning forest
πŸ‘€ T. Hutchcroft
πŸ“– Annales de l'Institut Henri PoincarΓ©, 2020

πŸ–₯ The Component Graph of the Uniform Spanning Forest: Transitions in Dimensions 9, 10, 11, ...
πŸ‘₯ T. Hutchcroft and Y. Peres
πŸ“– Probability Theory and Related Fields, 2019
🎬 Northwest Probability Seminar

First appeared 2016

πŸ–₯ Hyperbolic and Parabolic Unimodular Random Maps
πŸ‘₯ O. Angel, T. Hutchcroft, A. Nachmias, and G. Ray
πŸ“– Geometric and Functional Analysis, 2018
🎬 Isaac Newton Institute

πŸ–₯ Critical percolation on any quasi-transitive graph of exponential growth has no infinite clusters
πŸ‘€ T. Hutchcroft
πŸ“– Comptes Rendus Mathematique, 2016
🎬 Elegance in Probability

πŸ–₯ Uniform Spanning Forests of Planar Graphs
πŸ‘₯ T. Hutchcroft and A. Nachmias
πŸ“– Forum of Mathematics Sigma, 2019
🎬 Isaac Newton Institute

First appeared 2015

πŸ–₯ Interlacements and the Wired Uniform Spanning Forest
πŸ‘€ T. Hutchcroft
πŸ“– Annals of Probability, 2018
🎬 CIRM | OOPS Course

πŸ–₯ Boundaries of Planar Graphs: A Unified Approach
πŸ‘₯ T. Hutchcroft and Y. Peres
πŸ“– Electronic Journal of Probability, 2017

πŸ–₯ Indistinguishability of Trees in Uniform Spanning Forests
πŸ‘₯ T. Hutchcroft and A. Nachmias
πŸ“– Probability Theory and Related Fields, 2017
🎬 Banff

πŸ–₯ Collisions of Random Walks in Reversible Random Graphs
πŸ‘₯ T. Hutchcroft and Y. Peres
πŸ“– Electronic Communications in Probability, 2015

πŸ–₯ Wired Cycle-Breaking Dynamics for Uniform Spanning Forests
πŸ‘€ T. Hutchcroft
πŸ“– Annals of Probability, 2016

πŸ–₯ Unimodular Hyperbolic Triangulations: Circle Packing and Random Walk
πŸ‘₯ O. Angel, T. Hutchcroft, A. Nachmias, and G. Ray
πŸ“– Inventiones Mathematicae, 2016
🎬 Banff

Other Writing

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


Awards and Honours