Duncan Dauvergne

Department of Mathematics
University of Toronto
40 St. George St.
Toronto, Ontario, M5S2E4 Picture not found

Email: firstname.lastname@utoronto.ca

Offices: HU1025 (St. George campus) and DH-3062 (Mississauga)


I am an Assistant Professor in the Department of Mathematics at the University of Toronto. I am interested in probability and related areas. My main research areas include last passage percolation and the KPZ universality class, interacting particle systems, infection models built on seas of random walks, random sorting networks, and random polynomials.

Here is a recent CV (updated September 2021).

Publications and preprints

Last passage percolation and the KPZ universality class

  • Dauvergne, D. Non-uniqueness times for the maximizer of the KPZ fixed point. arXiv link.
  • Dauvergne, D., Nica, M. and Virág, B. RSK in last passage percolation: a unified approach. Probab. Surv. arXiv link.
  • Dauvergne, D. Last passage isometries for the directed landscape. arXiv link.
  • Dauvergne, D and Virág, B. The scaling limit of the longest increasing subsequence. arXiv link.
  • Dauvergne, D. and Zhang, L. Disjoint optimizers and the directed landscape. arXiv link.
    • Relevant talk: Building the directed landscape (Feb 2021): The link contains two talks from the One World Probability Seminar. The first is by Bálint Virág, and is a general introduction to random planar growth models, the KPZ universality class, and the world of the directed landscape. The second talk is my own; I go into detail about the construction of the directed landscape and then discuss newer results from the above paper with Lingfu Zhang.
  • Dauvergne, D., Sarkar, S., and Virág, B. Three-halves variation of geodesics in the directed landscape. Ann. Probab. (to appear) arXiv link.
  • Dauvergne, D. Hidden invariance of last passage percolation and directed polymers. Ann. Probab. arXiv link.
  • Dauvergne, D., Nica, M., and Virág, B. Uniform convergence to the Airy line ensemble. arXiv link.
  • Dauvergne, D., Ortmann, J., and Virág, B. The directed landscape. Acta Math. (to appear) arXiv link.
    • Relevant talk: The Airy sheet (June 2020): The Airy sheet is the scaling limit of last passage percolation between distinct spatial locations. Its construction comprises the first half of our paper `The directed landscape'. The directed landscape itself is built from metricly composing independent Airy sheets.
  • Dauvergne, D., and Virág, B. Bulk properties of the Airy line ensemble. Ann. Probab. arXiv link.

Infection spread amongst random walks

  • Dauvergne, D., and Sly, A. Spread of infections in a heterogeneous moving population. arXiv link.

Random sorting networks

Random polynomials

Other research

  • Dauvergne, D. Not every transitively D-space is D. Topology Appl. Link.
  • Dauvergne, D. and Edelstein-Keshet, L. Application of quasi-steady state methods to molecular motor transport on microtubules in fungal hyphae. J. Theoret. Biol. Link.


  • Winter 2022: MAT 402 (UTM) Geometry
  • Fall 2021: MAT 1600 (UTSG) Graduate Probability I

A few pictures

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Which is which? A directed geodesic, its weight function, and a Brownian bridge.

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A wiring diagram for the sorting network in S4 with swap sequence (2 3 1 2 1 3).

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Selected trajectories in the rescaled wiring diagram of a random 2000-element sorting network. Observe the sine curves...

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A 'susceptible-infected-recovered' infection model in a moving population. Particles that have recovered are not shown.