Limit theorems for random non-uniformly expanding or hyperbolic maps with exponential tails

Yeor Hafouta

RECORD

Limit theorems for random non-uniformly expanding or hyperbolic maps with exponential tails

Yeor Hafouta

Dynamical Systems · Submitted 13 Aug 2020

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

The authors' main claim We prove a Berry-Esseen theorem, a local central limit theorem and (local) large and (global) moderate deviations principles for i.i.d.

how it is stated · asserted 1.00 read the record →

Comment (0) Read on arXiv ↗

Cite ▾

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, 3,570 input tokens.

What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.15 · human participants 0.02 · controlled comparison 0.02 · randomized assignment 0.10 · states quantitative result 0.19 · compares with prior results 0.13 · mentions code or data availability 0.01.

The abstract, sentence by sentence

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

We prove a Berry-Esseen theorem, a local central limit theorem and (local) large and (global) moderate deviations principles for i.i.d. (uniformly) random non-uniformly expanding or hyperbolic maps with exponential first return times. Using existing results the problem is reduced to certain random (Young) tower extensions, which is the main focus of this paper. On the random towers we will obtain our results using contraction properties of random complex equivariant cones with respect to the complex Hilbert projective metric.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	We prove a Berry-Esseen theorem, a local central limit theorem and (local) large and (global) moderate deviations principles for i.i.d.	result 0.66	0.92	0.74	asserted 1.00
s1	(uniformly) random non-uniformly expanding or hyperbolic maps with exponential first return times.	contribution 0.60	0.16	0.09	unclear 0.73
s2	Using existing results the problem is reduced to certain random (Young) tower extensions, which is the main focus of this paper.	method 0.57	0.47	0.08	asserted 1.00
s3	On the random towers we will obtain our results using contraction properties of random complex equivariant cones with respect to the complex Hilbert projective metric.	method 0.99	0.82	0.12	asserted 0.97

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

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

We prove a Berry-Esseen theorem, a local central limit theorem and (local) large and (global) moderate deviations principles for i.i.d. (uniformly) random non-uniformly expanding or hyperbolic maps with exponential first return times. Using existing results the problem is reduced to certain random (Young) tower extensions, which is the main focus of this paper. On the random towers we will obtain our results using contraction properties of random complex equivariant cones with respect to the complex Hilbert projective metric.

Human review

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

How the literature uses it

2 arXiv papers cite this in 3 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 · 2 sentences without a confident label

Cites it as background 1 paper

We refer to [ref] for a partial list of relatively recent results of this kind.

Large deviations, moment estimates and almost sure invariance principles for skew products with mixing base maps and expanding on the average fibers · Quenched limit theorems for random random dynamical systems · 0.99

What it cites · 13 sentences without a confident label

Uses the method or tool of 2 papers

By using [ref] we have that [equation] Therefore, the difference between the centered and non-centered sum is $O(1/√(n))$.

On Eagleson's theorem in the non-stationary setup · A Berry-Esseen theorem · 0.85
The proof proceeds similarly to the proof of [ref] .

A local limit theorem for number of multiple recurrences generated by some mixing processes with applications to Young towers · Proof of Theorem [ref] · 0.90

Cites as background 1 paper

Recently (see [ref] and references therein) there has been a growing interest in additional limit theorems for random expanding or hyperbolic dynamical systems.

Almost sure invariance principle for random dynamical systems via Gou\"ezel 's approach · Introduction · 0.89

Discussion

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