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The directed landscape

- Duncan Dauvergne, Janosch Ortmann, B'alint Vir'ag
- Mathematics, Physics
- 2 December 2018

The conjectured limit of last passage percolation is a scale-invariant, independent, stationary increment process with respect to metric composition. We prove this for Brownian last passage… Expand

56 7- PDF

Basic properties of the Airy line ensemble

- Duncan Dauvergne, B'alint Vir'ag
- Mathematics, Physics
- 2 December 2018

The Airy line ensemble is a central object in random matrix theory and last passage percolation defined by a determinantal formula. The goal of this paper to make it more accessible to probabilists.… Expand

21 4- PDF

The local limit of random sorting networks

- O. Angel, Duncan Dauvergne, A. Holroyd, B'alint Vir'ag
- Mathematics
- 27 February 2017

A sorting network is a geodesic path from $12 \cdots n$ to $n \cdots 21$ in the Cayley graph of $S_n$ generated by adjacent transpositions. For a uniformly random sorting network, we establish the… Expand

11 2- PDF

Application of quasi-steady state methods to molecular motor transport on microtubules in fungal hyphae.

- Duncan Dauvergne, L. Edelstein-Keshet
- Biology, Medicine
- Journal of theoretical biology
- 21 August 2015

We consider bidirectional transport of cargo by molecular motors dynein and kinesin that walk along microtubules, and/or diffuse in the cell. The motors compete to transport cargo in opposite… Expand

6 1

The scaling limit of the longest increasing subsequence

- Duncan Dauvergne, B'alint Vir'ag
- Mathematics, Physics
- 16 April 2021

We provide a framework for proving convergence to the directed landscape, the central object in the Kardar-Parisi-Zhang universality class. For last passage models, we show that compact convergence… Expand

4 1- PDF

Universality for zeros of random polynomials

- T. Bloom, Duncan Dauvergne
- Mathematics
- 30 January 2018

We consider random polynomials of the form $H_n(z)=\sum_{j=0}^n\xi_jq_j(z)$ where the $\{\xi_j\}$ are i.i.d non-degenerate complex random variables, and the $\{q_j(z)\}$ are orthonormal polynomials… Expand

3 1

Uniform convergence to the Airy line ensemble

- Duncan Dauvergne, M. Nica, B'alint Vir'ag
- Mathematics, Physics
- 23 July 2019

We show that classical integrable models of last passage percolation and the related nonintersecting random walks converge uniformly on compact sets to the Airy line ensemble. Our core approach is to… Expand

11 1- PDF

Three-halves variation of geodesics in the directed landscape

- Duncan Dauvergne, S. Sarkar, B'alint Vir'ag
- Mathematics
- 24 October 2020

We show that geodesics in the directed landscape have $3/2$-variation and that weight functions along the geodesics have cubic variation.
We show that the geodesic and its landscape environment… Expand

2 1- PDF

The Archimedean limit of random sorting networks

- Duncan Dauvergne
- Mathematics
- 25 February 2018

A sorting network (also known as a reduced decomposition of the reverse permutation), is a shortest path from $12 \cdots n$ to $n \cdots 21$ in the Cayley graph of the symmetric group $S_n$ generated… Expand

16- PDF

Circular support in random sorting networks

- Duncan Dauvergne, B'alint Vir'ag
- Mathematics
- 25 February 2018

A sorting network is a shortest path from $12 \cdots n$ to $n \cdots 2 1$ in the Cayley graph of the symmetric group generated by adjacent transpositions. For a uniform random sorting network, we… Expand

9- PDF

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