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Continuous time random walks and L\'{e}vy walks with stochastic resetting

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Tian Zhou, Pengbo Xu, Weihua Deng

Statistical Mechanics · Submitted 13 Sep 2019

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

The authors' main claim The mean squared displacements of the CTRW and L\'{e}vy walks with stochastic resetting are calculated, uncovering that the stochastic resetting always makes the CTRW process localized and L\'{e}vy walk diffuse slower.

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arXiv ID1909.07213 (version 3)
Pith IDBHA7AUG7, Pith's permanent record of this paper and its review
CitationPengbo Xu, Tian Zhou, Weihua Deng. "Continuous time random walks and L\'{e}vy walks with stochastic resetting." arXiv:1909.07213 (2019). https://pith.science/paper/BHA7AUG7
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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 3,714 input tokens.

What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.07 · human participants 0.02 · controlled comparison 0.18 · randomized assignment 0.02 · states quantitative result 0.26 · compares with prior results 0.18 · mentions code or data availability 0.02.

The abstract, sentence by sentence

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

Intermittent stochastic processes appear in a wide field, such as chemistry, biology, ecology, and computer science. This paper builds up the theory of intermittent continuous time random walk (CTRW) and L\'{e}vy walk, in which the particles are stochastically reset to a given position with a resetting rate $r$. The mean squared displacements of the CTRW and L\'{e}vy walks with stochastic resetting are calculated, uncovering that the stochastic resetting always makes the CTRW process localized and L\'{e}vy walk diffuse slower. The asymptotic behaviors of the probability density function of L\'evy walk with stochastic resetting are carefully analyzed under different scales of $x$, and a striking influence of stochastic resetting is observed.

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 Intermittent stochastic processes appear in a wide field, such as chemistry, biology, ecology, and computer science. background 1.00 0.03 0.01 asserted 1.00
s1 This paper builds up the theory of intermittent continuous time random walk (CTRW) and L\'{e}vy walk, in which the particles are stochastically reset to a given position with a resetting rate $r$. contribution 0.98 0.92 0.06 asserted 0.98
s2 The mean squared displacements of the CTRW and L\'{e}vy walks with stochastic resetting are calculated, uncovering that the stochastic resetting always makes the CTRW process localized and L\'{e}vy walk diffuse slower. result 1.00 0.94 0.79 asserted 1.00
s3 The asymptotic behaviors of the probability density function of L\'evy walk with stochastic resetting are carefully analyzed under different scales of $x$, and a striking influence of stochastic resetting is observed. result 0.53 0.93 0.11 asserted 0.99

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

Intermittent stochastic processes appear in a wide field, such as chemistry, biology, ecology, and computer science. This paper builds up the theory of intermittent continuous time random walk (CTRW) and L\'{e}vy walk, in which the particles are stochastically reset to a given position with a resetting rate $r$. The mean squared displacements of the CTRW and L\'{e}vy walks with stochastic resetting are calculated, uncovering that the stochastic resetting always makes the CTRW process localized and L\'{e}vy walk diffuse slower. The asymptotic behaviors of the probability density function of L\'evy walk with stochastic resetting are carefully analyzed under different scales of $x$, and a striking influence of stochastic resetting is observed.

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2 arXiv papers cite this in 2 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it · 1 sentence without a confident label

Cites it as background 1 paper
  • The first study of resetting has been devoted to Brownian motion [ref] as a displacement process, later the discussion has been generalized for other types of motion, such as Lévy flights [ref] , Lévy walks [ref] , scaled Brownian motion (SBM) [ref] , and continuous time random walks (CTRW) [ref] .

    Continuous time random walks under power-law resetting · Introduction · 0.98

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