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Stationary fluctuations for a multi-species zero range process with long jumps

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Linjie Zhao

Probability · Submitted 16 Mar 2023

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

The authors' main claim We prove that for $0 < \alpha < 3/2$, the density fluctuation fields converge to the stationary solution of a coupled fractional Ornstein-Uhlenbeck process, and for $\alpha=3/2$, the limit points are concentrated on stationary energy solutions to a coupled fractional Burgers equation.

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arXiv ID2303.09110 (version 1)
Pith IDHZVPMSKG, Pith's permanent record of this paper and its review
CitationLinjie Zhao. "Stationary fluctuations for a multi-species zero range process with long jumps." arXiv:2303.09110 (2023). https://pith.science/paper/HZVPMSKG
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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 3,126 input tokens.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.32 · human participants 0.01 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.80 · compares with prior results 0.05 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; .

We consider stationary fluctuations for the multi-species zero range process with long jumps in one dimension, where the underlying transition probability kernel is $p(x) = c_+ |x|^{-1-\alpha}$ if $x > 0$ and $= c_-|x|^{-1-\alpha}$ if $x < 0$. Above, $c_{\pm} \geq 0, \alpha > 0$ are parameters. We prove that for $0 < \alpha < 3/2$, the density fluctuation fields converge to the stationary solution of a coupled fractional Ornstein-Uhlenbeck process, and for $\alpha=3/2$, the limit points are concentrated on stationary energy solutions to a coupled fractional Burgers equation.

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 stationary fluctuations for the multi-species zero range process with long jumps in one dimension, where the underlying transition probability kernel is $p(x) = c_+ |x|^{-1-\alpha}$ if $x > 0$ and $= c_-|x|^{-1-\alpha}$ if $x < 0$. contribution 0.50 0.33 0.04 asserted 0.81
s1 Above, $c_{\pm} \geq 0, \alpha > 0$ are parameters. background 0.96 0.11 0.02 asserted 0.89
s2 We prove that for $0 < \alpha < 3/2$, the density fluctuation fields converge to the stationary solution of a coupled fractional Ornstein-Uhlenbeck process, and for $\alpha=3/2$, the limit points are concentrated on stationary energy solutions to a coupled fractional Burgers equation. result 0.99 0.95 0.95 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 stationary fluctuations for the multi-species zero range process with long jumps in one dimension, where the underlying transition probability kernel is $p(x) = c_+ |x|^{-1-\alpha}$ if $x > 0$ and $= c_-|x|^{-1-\alpha}$ if $x < 0$. Above, $c_{\pm} \geq 0, \alpha > 0$ are parameters. We prove that for $0 < \alpha < 3/2$, the density fluctuation fields converge to the stationary solution of a coupled fractional Ornstein-Uhlenbeck process, and for $\alpha=3/2$, the limit points are concentrated on stationary energy solutions to a coupled fractional Burgers equation.

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