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The crossover regime for the weakly asymmetric simple exclusion process

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Tomohiro Sasamoto, Herbert Spohn

Statistical Mechanics · Submitted 9 Feb 2010

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim For this parameter window we obtain the limiting distribution function of the integrated current in terms of an integral over the difference of two Fredholm determinants.

how it is stated · asserted 1.00 read the record →

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arXiv ID1002.1873 (version 3)
Pith IDWBTN73H7, Pith's permanent record of this paper and its review
CitationHerbert Spohn, Tomohiro Sasamoto. "The crossover regime for the weakly asymmetric simple exclusion process." arXiv:1002.1873 (2010). https://pith.science/paper/WBTN73H7
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What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.13 · human participants 0.01 · controlled comparison 0.03 · randomized assignment 0.01 · states quantitative result 0.69 · compares with prior results 0.26 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v3. Results and the main claim are underlined; .

We consider the asymmetric simple exclusion process in one dimension with weak asymmetry (WASEP) and 0-1 step initial condition. Our interest are the fluctuations of the time-integrated particle current at some prescribed spatial location. One expects a crossover from Gaussian to Tracy-Widom distributed fluctuations. The appropriate crossover scale is an asymmetry of order $\epsilon^{-1/2}$, times of order $\epsilon^{-2}$, and a spatial location of order $\epsilon^{-3/2}$. For this parameter window we obtain the limiting distribution function of the integrated current in terms of an integral over the difference of two Fredholm determinants. For large times, on the scale $\epsilon^{-2}$, this distribution function converges to the one of Tracy-Widom.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 We consider the asymmetric simple exclusion process in one dimension with weak asymmetry (WASEP) and 0-1 step initial condition. background 0.78 0.43 0.03 asserted 0.78
s1 Our interest are the fluctuations of the time-integrated particle current at some prescribed spatial location. contribution 0.63 0.28 0.03 asserted 0.92
s2 One expects a crossover from Gaussian to Tracy-Widom distributed fluctuations. background 0.96 0.06 0.13 hedged possibility 0.89
s3 The appropriate crossover scale is an asymmetry of order $\epsilon^{-1/2}$, times of order $\epsilon^{-2}$, and a spatial location of order $\epsilon^{-3/2}$. result 0.76 0.28 0.23 asserted 1.00
s4 For this parameter window we obtain the limiting distribution function of the integrated current in terms of an integral over the difference of two Fredholm determinants. result 0.98 0.94 0.67 asserted 1.00
s5 For large times, on the scale $\epsilon^{-2}$, this distribution function converges to the one of Tracy-Widom. result 0.98 0.85 0.27 asserted 1.00

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 1.00.

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Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper
Original abstract

We consider the asymmetric simple exclusion process in one dimension with weak asymmetry (WASEP) and 0-1 step initial condition. Our interest are the fluctuations of the time-integrated particle current at some prescribed spatial location. One expects a crossover from Gaussian to Tracy-Widom distributed fluctuations. The appropriate crossover scale is an asymmetry of order $\epsilon^{-1/2}$, times of order $\epsilon^{-2}$, and a spatial location of order $\epsilon^{-3/2}$. For this parameter window we obtain the limiting distribution function of the integrated current in terms of an integral over the difference of two Fredholm determinants. For large times, on the scale $\epsilon^{-2}$, this distribution function converges to the one of Tracy-Widom.

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5 arXiv papers cite this in 8 sentences

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