13 citations · 28 across the 9 of their papers we have counts for
11 papers
Classification of the eternal solutions and multiple coalescing shocks in the KPZ fixed point
Sudeshna Bhattacharjee, Ofer Busani, Evan Sorensen
We give a complete classification of the eternal solutions for the KPZ fixed point. Each of these is a (possibly infinite) max-plus convolution of the known eternal solutions, call…
Scaling limit of multi-type invariant measures via the directed landscape
Ofer Busani, Timo Seppäläinen, Evan Sorensen
This paper studies the large scale limits of multi-type invariant distributions and Busemann functions of planar stochastic growth models in the Kardar-Parisi-Zhang (KPZ) class. We…
Jointly invariant measures for the Kardar-Parisi-Zhang Equation
Sean Groathouse, Firas Rassoul-Agha, Timo Seppäläinen +1
We give an explicit description of the jointly invariant measures for the KPZ equation. These are couplings of Brownian motions with drift, and can be extended to a process defined…
The stationary horizon as the central multi-type invariant measure in the KPZ universality class
Evan Sorensen
The Kardar-Parisi-Zhang (KPZ) universality class describes a large class of 2-dimensional models of random growth, which exhibit universal scaling exponents and limiting statistics…
Scaling limit of the TASEP speed process
Ofer Busani, Timo Seppäläinen, Evan Sorensen
We show that the multi-type stationary distribution of the totally asymmetric simple exclusion process (TASEP) scales to a nontrivial limit around the Bernoulli measure of density…
The stationary horizon and semi-infinite geodesics in the directed landscape
Ofer Busani, Timo Seppäläinen, Evan Sorensen
The stationary horizon (SH) is a stochastic process of coupled Brownian motions indexed by their real-valued drifts. It was first introduced by the first author as the diffusive sc…
Global structure of semi-infinite geodesics and competition interfaces in Brownian last-passage percolation
Timo Seppäläinen, Evan Sorensen
In Brownian last-passage percolation (BLPP), the Busemann functions are indexed by two points $\mathbf x,\mathbf y \in \mathbb Z \times \mathbb…
Busemann process and semi-infinite geodesics in Brownian last-passage percolation
Timo Seppäläinen, Evan Sorensen
We prove the existence of semi-infinite geodesics for Brownian last-passage percolation (BLPP). Specifically, on a single event of probability one, there exist semi-infinite geodes…
Interlacing Properties of Coefficient Polynomials in Differential Operator Representations of Real-Root Preserving Linear Transformations
David A. Cardon, Evan L. Sorensen, Jason C. White
We study linear transformations of the form where is a real orthogonal polynomial system. Such transformatio…
On Zero-Sector Reducing Operators
David A. Cardon, Tamás Forgács, Andrzej Piotrowski +2
We prove a Jensen-disc type theorem for polynomials having all their zeros in a sector of the complex plane. This result is then used to prove the existence of…
Real-Root Preserving Differential Operator Representations of Orthogonal Polynomials
David A. Cardon, Evan L. Sorensen, Jason C. White
In this paper, we study linear transformations of the form where is an orthogonal polynomial system. Of particular interest is understanding when these…