Fluctuation Properties of the TASEP with Periodic Initial Configuration

By Alexei Borodin, P. Ferrari, Michael Praehofer, Tomohiro Sasamoto. 2006

284 citations recorded by the source corpus.

Abstract We consider the joint distributions of particle positions for the continuous time totally asymmetric simple exclusion process (TASEP). They are expressed as Fredholm determinants with a kernel defining a signed determinantal point process. We then consider certain periodic initial conditions and determine the kernel in the scaling limit. This result has been announced first in a letter by one of us (Sasamoto in J. Phys. A 38:L549–L556, 2005) and here we provide a self-contained derivation. Connections to last passage directed percolation and random matrices are also briefly discussed.

Subfields: Condensed Matter Physics, Mathematical Physics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/e738cf7fc124fac844c7c7fce53fefe0f88a9cee

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Condensed Matter Physics

In Mathematical Physics

In Statistics and Probability

Citations in the corpus

The One-Dimensional KPZ Equation and Its Universality Class (2015, background): “For PNG, TASEP, and the zero temperature semi-discrete directed polymer the large time statistics starting from flat initial conditions have been investigated [43–46].”
Non-equilibrium steady states: fluctuations and large deviations of the density and of the current (2007, background): “Concerning the fluctuations or the large deviations of the current of driven diffusive systems, there has been lots of progress over the last ten years [136]–[ 141 ].”
Evidence for Geometry-Dependent Universal Fluctuations of the Kardar-Parisi-Zhang Interfaces in Liquid-Crystal Turbulence (2012, methodology): “In contrast, Ferrari and Frings studied finite-time fluctuations of the TASEP, the PASEP and the PNG model, and showed that the leading correction is again O(t−1/3) for the first-order cumulant [4, 26], with the positive sign for the TASEP like in our experiment.”
Introduction to KPZ (2011, background): “) Airy1 arises in growth models starting from flat initial data and point-to-line random polymers [105],[23].”
A pedestrian's view on interacting particle systems, KPZ universality and random matrices (2008, methodology): “In line with the nomenclature used to designate the corresponding single-point distributions (TW2 for case III and TW1 for case I), the two processes are now called Airy2 and Airy1 processes, respectively [24, 25, 23, 50].”
Large time asymptotics of growth models on space-like paths I: PushASEP (2007, methodology): “3 in [4] we can further reduce the summation domain to e D(t i) without changing the result.”
Height Fluctuations for the Stationary KPZ Equation (2014, unknown): “These statistical properties agreed between the models, but depended non-trivially on the type of initial data or geometry for the growth models, such as curved [6, 10, 21, 22, 60, 61, 68], flat [10, 21, 23–25, 43, 48, 73] or stationary [7–9, 47, 49, 57, 69].”
An appetizer to modern developments on the Kardar–Parisi–Zhang universality class (2017, background): “Analytic expressions for such limiting processes have been obtained for the the circular and flat subclasses [70], and named the Airy2 processA2(ζ) for the circular case [66, 97] and the Airy1 processA1(ζ) for the flat case [83, 98].”