Current Fluctuations for the Totally Asymmetric Simple Exclusion Process

By Michael Praehofer, Herbert Spohn. 2001

191 citations recorded by the source corpus.

The time-integrated current of the TASEP has non-Gaussian fluctuations of order t1/3. The recently discovered connection to random matrices and the Painleve II Riemann-Hilbert problem provides a technique through which we obtain the probability distribution of the current fluctuations, in particular their dependence on initial conditions, and the stationary two-point function. Some open problems are explained.

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

View Paper: https://www.semanticscholar.org/paper/697fb4911a29c3c1593705dcd5d3abb957fe2a52

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In Condensed Matter Physics

In Mathematical Physics

In Statistics and Probability

Citations in the corpus

Phase transition of the largest eigenvalue for nonnull complex sample covariance matrices (2004, methodology): “The last passage percolation model considered in [5, 33] has some relevance to our problem; see Section 6 below.”
A pedestrian's view on interacting particle systems, KPZ universality and random matrices (2008, methodology): “4), Prähofer and Spohn show that the resulting fluctuation distribution is identical (under the rescaling prescribed by KPZ theory) to that obtained by Johansson for the dTASEP.”
A Fredholm Determinant Representation in ASEP (2008, background): “For further discussion of this universal regime see [6, 11].”
Scaling Limit for the Space-Time Covariance of the Stationary Totally Asymmetric Simple Exclusion Process (2005, background): “[19] With the above definitions Q({G(m,n) ≤ t}) = PTA({m+ n ≤ ht(m− n)}).”
Stochastic Interface Models (2005, methodology): “The randomly growing Young diagram is equivalent to the totally asymmetric one dimensional exclusion process (first observed by Rost, see also [215], [90]), the last-passage directed percolation model and it is related to the Hammersley’s model [157], domino tilings and dimer model [160].”
Exact Scaling Functions for One-Dimensional Stationary KPZ Growth (2002, background): “But they have been discussed already elsewhere [5, 6, 7].”
The Kardar-Parisi-Zhang equation and universality class (2011, background): “If the path measure underlying the polymer is a nearest neighbor random walk, and the noise is formed from IID exponential random variable weights, then there is an exact coupling between LPP and the totally asymmetric corner growth model started with a wedge (see for example [136] or [19]).”
Scaling for a one-dimensional directed polymer with boundary conditions (2009, background): “The recent article [5] verifies a complete picture proposed in [28] that characterizes the scaling limits of Gm,n with exponential weights as a function of the parameters of the boundary weights and the ratio m/n.”