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Returns to origin of a one-dimensional random walk visiting each site an even number of times

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G.M. Cicuta, M.Contedini

Probability · Submitted 11 Mar 1999

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

The authors' main claim We call this class the even-visiting random walks and provide a closed expression to evaluate them.

how it is stated · asserted 1.00 read the record →

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arXiv IDmath/9903063 (version 1)
Pith IDKQHFEZVO, Pith's permanent record of this paper and its review
CitationG.M. Cicuta, M.Contedini. "Returns to origin of a one-dimensional random walk visiting each site an even number of times." arXiv:math/9903063 (1999). https://pith.science/paper/KQHFEZVO
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The compiled record

The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 2,276 input tokens.

What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.14 · human participants 0.02 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.18 · compares with prior results 0.04 · mentions code or data availability 0.02.

The abstract, sentence by sentence

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

The class of random walks in one dimension, returning to the origin, restricted by the requirement that any site visited (different from the origin) is visited an even number of times, is analyzed in the present note. We call this class the even-visiting random walks and provide a closed expression to evaluate them.

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 The class of random walks in one dimension, returning to the origin, restricted by the requirement that any site visited (different from the origin) is visited an even number of times, is analyzed in the present note. contribution 0.77 0.79 0.13 asserted 0.94
s1 We call this class the even-visiting random walks and provide a closed expression to evaluate them. contribution 0.97 0.94 0.45 asserted 1.00

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

What was examined, and what was not

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not examined
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  • figures and tables
  • references and citing sentences
  • relations to other papers
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  • P abstract
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  • S sections
  • T body sentences
  • C citations
  • R cross-paper relations

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

The class of random walks in one dimension, returning to the origin, restricted by the requirement that any site visited (different from the origin) is visited an even number of times, is analyzed in the present note. We call this class the even-visiting random walks and provide a closed expression to evaluate them.

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