Duncan Dauvergne

Publications and preprints

The directed landscape

• Dauvergne, D. The 27 geodesic networks in the directed landscape. arXiv link.
• Dauvergne, D. Last passage isometries for the directed landscape. Probab. Theory Related Fields arXiv link.
• Dauvergne, D and Virág, B. The scaling limit of the longest increasing subsequence. arXiv link.
• Relevant talk: The scaling limit of the longest increasing subsequence (Sep 2020)
• Dauvergne, D. and Zhang, L. Disjoint optimizers and the directed landscape. Mem. Amer. Math. Soc. 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. arXiv link.
• Dauvergne, D., Ortmann, J., and Virág, B. The directed landscape. Acta Math. 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.

The Airy line ensemble

• Dauvergne, D. Wiener densities for the Airy line ensemble. arXiv link.
• Dauvergne, D., Nica, M., and Virág, B. Uniform convergence to the Airy line ensemble. Ann. Inst. H. Poincaré Probab. Statist. (to appear) arXiv link.
• Dauvergne, D., and Virág, B. Bulk properties of the Airy line ensemble. Ann. Probab. arXiv link.

Other work on 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. Hidden invariance of last passage percolation and directed polymers. Ann. Probab. arXiv link.
• Relevant talk: Hidden invariance of last passage percolation and directed polymers (May 2020)

Infection spread amongst random walks

• Dauvergne, D., and Sly, A. The SIR model in a moving population: propagation of infection and herd immunity. arXiv link.
• Relevant talk: Infection spread in a sea of random walks (May 2021)
• Dauvergne, D., and Sly, A. Spread of infections in a heterogeneous moving population. arXiv link.

Random sorting networks

• Dauvergne, D. The Archimedean limit of random sorting networks. J. Amer. Math. Soc. arXiv link.
• Relevant set of slides: The Archimedean limit of random sorting networks (March 2019)
• Dauvergne, D. and Virág, B. Circular support in random sorting networks. Trans. Amer. Math. Soc. arXiv link.
• Angel, O., Dauvergne, D., Holroyd, A.E., and Virág, B. The local limit of random sorting networks. Ann. Inst. H. Poincaré Probab. Statist. arXiv link.

Random polynomials

• Dauvergne, D. A necessary and sufficient condition for global convergence of the zeros of random polynomials. Adv. Math. arXiv link.
• Relevant talk: Zeros of random sums of orthogonal polynomials (August 2019)
• Bloom, T. and Dauvergne, D. Asymptotic zero distribution of random orthogonal polynomials. Ann. Probab. arXiv link.

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.

Teaching

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

A few pictures

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

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

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

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