The semi-infinite asymmetric exclusion process

Large deviations via matrix products

Horacio Gonzalez Duhart Muñoz De Cote, Peter Morters, Johannes Zimmer

Research output: Contribution to journalArticle

1 Citation (Scopus)
17 Downloads (Pure)

Abstract

We study the totally asymmetric exclusion process on the positive integers with a single particle source at the origin. Liggett (1975) has shown that the long term behaviour of this process has a phase transition: If the particle production rate at the source and the original density are below a critical value, the stationary measure is a product measure, otherwise the stationary measure is spatially correlated. Following the approach of Derrida et al. (1993) it was shown by Grosskinsky (2004) that these correlations can be described by means of a matrix product representation. In this paper we derive a large deviation principle with explicit rate function for the particle density in a macroscopic box based on this representation. The novel and rigorous technique we develop for this problem combines spectral theoretical and combinatorial ideas and is potentially applicable to other models described by matrix products.
Original languageEnglish
Pages (from-to)301-323
JournalPotential Analysis
Volume48
Issue number3
Early online date29 Jun 2017
DOIs
Publication statusPublished - 1 Apr 2018

Fingerprint

Asymmetric Exclusion Process
Matrix Product
Large Deviations
Stationary Measure
Product Measure
Large Deviation Principle
Rate Function
Critical value
Phase Transition
Integer
Term
Model

Cite this

The semi-infinite asymmetric exclusion process : Large deviations via matrix products. / Gonzalez Duhart Muñoz De Cote, Horacio; Morters, Peter; Zimmer, Johannes.

In: Potential Analysis, Vol. 48, No. 3, 01.04.2018, p. 301-323.

Research output: Contribution to journalArticle

Gonzalez Duhart Muñoz De Cote, Horacio ; Morters, Peter ; Zimmer, Johannes. / The semi-infinite asymmetric exclusion process : Large deviations via matrix products. In: Potential Analysis. 2018 ; Vol. 48, No. 3. pp. 301-323.
@article{251f7d96bf1e4cfc87289cded8d2ae86,
title = "The semi-infinite asymmetric exclusion process: Large deviations via matrix products",
abstract = "We study the totally asymmetric exclusion process on the positive integers with a single particle source at the origin. Liggett (1975) has shown that the long term behaviour of this process has a phase transition: If the particle production rate at the source and the original density are below a critical value, the stationary measure is a product measure, otherwise the stationary measure is spatially correlated. Following the approach of Derrida et al. (1993) it was shown by Grosskinsky (2004) that these correlations can be described by means of a matrix product representation. In this paper we derive a large deviation principle with explicit rate function for the particle density in a macroscopic box based on this representation. The novel and rigorous technique we develop for this problem combines spectral theoretical and combinatorial ideas and is potentially applicable to other models described by matrix products.",
author = "{Gonzalez Duhart Mu{\~n}oz De Cote}, Horacio and Peter Morters and Johannes Zimmer",
year = "2018",
month = "4",
day = "1",
doi = "10.1007/s11118-017-9635-9",
language = "English",
volume = "48",
pages = "301--323",
journal = "Potential Analysis",
issn = "0926-2601",
publisher = "Springer Netherlands",
number = "3",

}

TY - JOUR

T1 - The semi-infinite asymmetric exclusion process

T2 - Large deviations via matrix products

AU - Gonzalez Duhart Muñoz De Cote, Horacio

AU - Morters, Peter

AU - Zimmer, Johannes

PY - 2018/4/1

Y1 - 2018/4/1

N2 - We study the totally asymmetric exclusion process on the positive integers with a single particle source at the origin. Liggett (1975) has shown that the long term behaviour of this process has a phase transition: If the particle production rate at the source and the original density are below a critical value, the stationary measure is a product measure, otherwise the stationary measure is spatially correlated. Following the approach of Derrida et al. (1993) it was shown by Grosskinsky (2004) that these correlations can be described by means of a matrix product representation. In this paper we derive a large deviation principle with explicit rate function for the particle density in a macroscopic box based on this representation. The novel and rigorous technique we develop for this problem combines spectral theoretical and combinatorial ideas and is potentially applicable to other models described by matrix products.

AB - We study the totally asymmetric exclusion process on the positive integers with a single particle source at the origin. Liggett (1975) has shown that the long term behaviour of this process has a phase transition: If the particle production rate at the source and the original density are below a critical value, the stationary measure is a product measure, otherwise the stationary measure is spatially correlated. Following the approach of Derrida et al. (1993) it was shown by Grosskinsky (2004) that these correlations can be described by means of a matrix product representation. In this paper we derive a large deviation principle with explicit rate function for the particle density in a macroscopic box based on this representation. The novel and rigorous technique we develop for this problem combines spectral theoretical and combinatorial ideas and is potentially applicable to other models described by matrix products.

U2 - 10.1007/s11118-017-9635-9

DO - 10.1007/s11118-017-9635-9

M3 - Article

VL - 48

SP - 301

EP - 323

JO - Potential Analysis

JF - Potential Analysis

SN - 0926-2601

IS - 3

ER -