Distribution of a Tagged Particle Position in the One-Dimensional Symmetric Simple Exclusion Process with Two-Sided Bernoulli Initial Condition

For the two-sided Bernoulli initial condition with density ρ - (resp. ρ + ) to the left (resp. to the right), we study the distribution of a tagged particle in the one dimensional symmetric simple exclusion process. We obtain a formula for the moment generating function of the associated current in...

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Bibliographic Details
Published in:Communications in mathematical physics 2021-06, Vol.384 (3), p.1409-1444
Main Authors: Imamura, Takashi, Mallick, Kirone, Sasamoto, Tomohiro
Format: Article
Language:English
Subjects:
Classical and Quantum Gravitation
Complex Systems
Density
Mathematical and Computational Physics
Mathematical Physics
Physics
Physics and Astronomy
Position measurement
Quantum Physics
Relativity Theory
Theoretical
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Summary:For the two-sided Bernoulli initial condition with density ρ - (resp. ρ + ) to the left (resp. to the right), we study the distribution of a tagged particle in the one dimensional symmetric simple exclusion process. We obtain a formula for the moment generating function of the associated current in terms of a Fredholm determinant. Our arguments are based on a combination of techniques from integrable probability which have been developed recently for studying the asymmetric exclusion process and a subsequent intricate symmetric limit. An expression for the large deviation function of the tagged particle position is obtained, including the case of the stationary measure with uniform density ρ .
ISSN:0010-3616
1432-0916
DOI:10.1007/s00220-021-03954-x