Pith. Sign in

RECORD

Unique ergodicity of simple symmetric random walks on the circle

PaperPDF from arXiv

data files

Paper breakdownThe authors' claims, conditions and measurements, as JSON Signed receiptProof this review has not been altered
X Bluesky LinkedIn Reddit Hacker News
Klaudiusz Czudek

Dynamical Systems · Submitted 4 Jan 2023

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

The authors' main claim In this note we present a new proof of latter result.

how it is stated · asserted 0.99 read the record →

Comment (0) Read on arXiv ↗
Cite ▾
arXiv ID2301.01496 (version 2)
Pith IDQP7O6DZN, Pith's permanent record of this paper and its review
CitationKlaudiusz Czudek. "Unique ergodicity of simple symmetric random walks on the circle." arXiv:2301.01496 (2023). https://pith.science/paper/QP7O6DZN
Claim paper

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.

Open the compiled record

Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 4,302 input tokens.

What the abstract itself states, as probabilities: claims first 0.05 · states limitation 0.10 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.03 · states quantitative result 0.04 · compares with prior results 0.87 · mentions code or data availability 0.01.

The abstract, sentence by sentence

arXiv listing abstract v2. Results and the main claim are underlined; .

Fix an irrational number $\alpha$ and a smooth, positive, real function $\mathfrak{p}$ on the circle. If current position is $x\in \mathbb R/\mathbb Z$ then in the next step jump to $x+\alpha$ with probability $\mathfrak{p}(x)$ or to $x-\alpha$ with probability $1-\mathfrak{p}(x)$. In 1999 Sinai has proven that if $\mathfrak{p}$ is asymmetric (in certain sense) or $\alpha$ is Diophantine then the Markov process possesses a unique stationary distribution. Next year Conze and Guivarc'h showed the uniqueness of stationary distribution for an arbitrary irrational angle $\alpha$. In this note we present a new proof of latter result.

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 Fix an irrational number $\alpha$ and a smooth, positive, real function $\mathfrak{p}$ on the circle. background 0.78 0.19 0.02 unclear 0.61
s1 If current position is $x\in \mathbb R/\mathbb Z$ then in the next step jump to $x+\alpha$ with probability $\mathfrak{p}(x)$ or to $x-\alpha$ with probability $1-\mathfrak{p}(x)$. background 0.51 0.07 0.02 asserted 0.95
s2 In 1999 Sinai has proven that if $\mathfrak{p}$ is asymmetric (in certain sense) or $\alpha$ is Diophantine then the Markov process possesses a unique stationary distribution. background 1.00 0.02 0.05 asserted 1.00
s3 Next year Conze and Guivarc'h showed the uniqueness of stationary distribution for an arbitrary irrational angle $\alpha$. background 1.00 0.03 0.11 asserted 1.00
s4 In this note we present a new proof of latter result. contribution 1.00 0.91 0.31 asserted 0.99

What kind of paper the classifier reports this is: theoretical result 0.99 · evidence from proof or derivation 0.93.

What was examined, and what was not

sources read
  • arXiv listing abstract v2
not examined
  • full text
  • figures and tables
  • references and citing sentences
  • relations to other papers
levels run
  • P abstract
not run
  • 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

Fix an irrational number $\alpha$ and a smooth, positive, real function $\mathfrak{p}$ on the circle. If current position is $x\in \mathbb R/\mathbb Z$ then in the next step jump to $x+\alpha$ with probability $\mathfrak{p}(x)$ or to $x-\alpha$ with probability $1-\mathfrak{p}(x)$. In 1999 Sinai has proven that if $\mathfrak{p}$ is asymmetric (in certain sense) or $\alpha$ is Diophantine then the Markov process possesses a unique stationary distribution. Next year Conze and Guivarc'h showed the uniqueness of stationary distribution for an arbitrary irrational angle $\alpha$. In this note we present a new proof of latter result.

Human review

How Pith checks papers → · Full audit of this paper →

How the literature uses it

1 arXiv paper cite this in 1 sentence

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

Discussion

Know something about this paper? Leave a comment, or highlight any passage above to comment on it.