1201 E California Blvd

Pasadena, CA 91125

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 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.

Math 191c: Random walks and uniform spanning trees. Graduate topics course. 18×(3/2) hours.

Caltech, Spring 2022. 📚 Notes

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

Cambridge, 2020. 📚 Notes 📝 Example Sheet 1 📝 Example Sheet 2 📝 Example Sheet 3

Uniform spanning forests in high dimension. Graduate mini-course. 3×1 hours.

Online Open Probability School, 2020. 🎬 Video 📚 Notes

Online Open Probability School, 2020. 🎬 Video 📚 Notes

🎬 A new approach to critical percolation, ICMP 2020.

🎬 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.

🎬 Philip Easo: *
Uniqueness of the giant component on finite transitive graphs*, Percolation Today 2021.

🎬 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.

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.

🖥 Uniqueness of the infinite tree in low-dimensional random forests

👥 N. Halberstam and T. Hutchcroft

📖 Preprint

👥 N. Halberstam and T. Hutchcroft

📖 Preprint

🖥 Double-exponential susceptibility growth in Dyson's hierarchical model with |x-y|^{-2} interaction

👥 P. Easo, T. Hutchcroft, and J. Kurrek*

📖 Preprint

👥 P. Easo, T. Hutchcroft, and J. Kurrek*

📖 Preprint

🖥 The number of ends in the uniform spanning tree for recurrent unimodular random graphs

👥 D. van Engelenberg and T. Hutchcroft

📖 Preprint

👥 D. van Engelenberg and T. Hutchcroft

📖 Preprint

🖥 Critical cluster volumes in hierarchical percolation

👤 T. Hutchcroft

📖 Preprint

🎬 Percolation Today

👤 T. Hutchcroft

📖 Preprint

🎬 Percolation Today

🖥 Logarithmic corrections to the Alexander-Orbach conjecture for the four-dimensional uniform spanning tree

👥 N. Halberstam and T. Hutchcroft

📖 Preprint

👥 N. Halberstam and T. Hutchcroft

📖 Preprint

🖥 Slightly supercritical percolation on nonamenable graphs II: Growth and isoperimetry of infinite clusters

👤 T. Hutchcroft

📖 Preprint

👤 T. Hutchcroft

📖 Preprint

🖥 On the boundary at infinity for branching random walk

👥 E. Candellero and T. Hutchcroft

📖 Preprint

👥 E. Candellero and T. Hutchcroft

📖 Preprint

🖥 Most transient random walks have infinitely many cut times

👥 N. Halberstam and T. Hutchcroft

📖 Preprint

👥 N. Halberstam and T. Hutchcroft

📖 Preprint

🖥 Supercritical percolation on finite transitive graphs I: Uniqueness of the giant component

👥 P. Easo and T. Hutchcroft

📖 Preprint

🎬 Stanford | Percolation Today

👥 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*

📖 Combinatorics, Probability, and Computing, 2022

👥 T. Hutchcroft, A. Kent*, and P. Nizić-Nikolac*

📖 Combinatorics, Probability, and Computing, 2022

🖥 High-dimensional near-critical percolation and the torus plateau

👥 T. Hutchcroft, E. Michta, and G. Slade

📖 Annals of Probability, 2023

🎬 Percolation Today

👥 T. Hutchcroft, E. Michta, and G. Slade

📖 Annals of Probability, 2023

🎬 Percolation Today

🖥 What are the limits of universality?

👥 N. Halberstam and T. Hutchcroft

📖 Proceedings of the Royal Society Series A, 2022

🎬 Percolation Today

👥 N. Halberstam and T. Hutchcroft

📖 Proceedings of the Royal Society Series A, 2022

🎬 Percolation Today

🖥 Non-triviality of the phase transition for percolation on finite transitive graphs

👥 T. Hutchcroft and M. Tointon

📖 Preprint

🎬 Percolation Today

👥 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

👤 T. Hutchcroft

📖 Preprint

🎬 Percolation Today

🖥 Logarithmic corrections to scaling in the four-dimensional uniform spanning tree

👥 T. Hutchcroft and P. Sousi

📖 Communications in Mathematical Physics, to appear

🎬 Oxford | Percolation Today | JIPS | OOPS Course

👥 T. Hutchcroft and P. Sousi

📖 Communications in Mathematical Physics, to appear

🎬 Oxford | Percolation Today | JIPS | OOPS Course

🖥 Collisions of random walks in dynamic random environments

👥 N. Halberstam and T. Hutchcroft

📖 Electronic Journal of Probability, 2022

👥 N. Halberstam and T. Hutchcroft

📖 Electronic Journal of Probability, 2022

🖥 Continuity of the Ising phase transition on nonamenable groups

👤 T. Hutchcroft

📖 Preprint

🎬 Percolation Today

👤 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

👥 O. Angel, T. Hutchcroft, and A. Járai

📖 Probability Theory and Related Fields, 2021

🖥 Percolation on hyperbolic graphs

👤 T. Hutchcroft

📖 Geometric and Functional Analysis, 2019

🎬 Courant Institute

👤 T. Hutchcroft

📖 Geometric and Functional Analysis, 2019

🎬 Courant Institute

🖥 Coalescing random walk on unimodular graphs

👥 E. Foxall, T. Hutchcroft, and M. Junge

📖 Electronic Communications in Probability, 2018

👥 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

👥 O. Angel, A.E. Holroyd, T. Hutchcroft, and A. Levy

📖 Canadian Journal of Mathematics, 2020

🖥 Statistical physics on a product of trees

👤 T. Hutchcroft

📖 Annales de l'Institut Henri Poincaré, 2019

👤 T. Hutchcroft

📖 Annales de l'Institut Henri Poincaré, 2019

🖥 Self-avoiding walk on nonunimodular transitive graphs

👤 T. Hutchcroft

📖 Annals of Probability, 2019

👤 T. Hutchcroft

📖 Annals of Probability, 2019

🖥 Finitely Dependent Cycle Coloring

👥 A.E. Holroyd, T. Hutchcroft, and A. Levy

📖 Electronic Communications in Probability, 2018

👥 A.E. Holroyd, T. Hutchcroft, and A. Levy

📖 Electronic Communications in Probability, 2018

🖥 Mallows Permutations and Finite Dependence

👥 A.E. Holroyd, T. Hutchcroft, and A. Levy

📖 Annals of Probability, 2020

👥 A.E. Holroyd, T. Hutchcroft, and A. Levy

📖 Annals of Probability, 2020

🖥 Hyperbolic and Parabolic Unimodular Random Maps

👥 O. Angel, T. Hutchcroft, A. Nachmias, and G. Ray

📖 Geometric and Functional Analysis, 2018

🎬 Isaac Newton Institute

👥 O. Angel, T. Hutchcroft, A. Nachmias, and G. Ray

📖 Geometric and Functional Analysis, 2018

🎬 Isaac Newton Institute

🖥 Uniform Spanning Forests of Planar Graphs

👥 T. Hutchcroft and A. Nachmias

📖 Forum of Mathematics Sigma, 2019

🎬 Isaac Newton Institute

👥 T. Hutchcroft and A. Nachmias

📖 Forum of Mathematics Sigma, 2019

🎬 Isaac Newton Institute

🖥 Interlacements and the Wired Uniform Spanning Forest

👤 T. Hutchcroft

📖 Annals of Probability, 2018

🎬 CIRM | OOPS Course

👤 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

👥 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

👥 T. Hutchcroft and A. Nachmias

📖 Probability Theory and Related Fields, 2017

🎬 Banff

🖥 Unimodular Hyperbolic Triangulations: Circle Packing and Random Walk

👥 O. Angel, T. Hutchcroft, A. Nachmias, and G. Ray

📖 Inventiones Mathematicae, 2016

🎬 Banff

👥 O. Angel, T. Hutchcroft, A. Nachmias, and G. Ray

📖 Inventiones Mathematicae, 2016

🎬 Banff

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