Weak containment and Rokhlin entropy

Brandon Seward

RECORD

Weak containment and Rokhlin entropy

Brandon Seward

Dynamical Systems · Submitted 22 Feb 2016

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

The authors' main claim We define a new notion of weak containment for joinings, and we show that this notion implies an inequality between relative Rokhlin entropies.

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, 2,887 input tokens.

What the abstract itself states, as probabilities: claims first 0.06 · states limitation 0.05 · human participants 0.02 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.32 · compares with prior results 0.11 · 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 define a new notion of weak containment for joinings, and we show that this notion implies an inequality between relative Rokhlin entropies. This leads to new upper bounds to Rokhlin entropy. We also use this notion to study how Pinsker algebras behave under direct products, and we study the Rokhlin entropy of restricted actions of finite-index subgroups.

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 define a new notion of weak containment for joinings, and we show that this notion implies an inequality between relative Rokhlin entropies.	contribution 0.91	0.96	0.60	asserted 1.00
s1	This leads to new upper bounds to Rokhlin entropy.	result 0.89	0.91	0.22	asserted 0.99
s2	We also use this notion to study how Pinsker algebras behave under direct products, and we study the Rokhlin entropy of restricted actions of finite-index subgroups.	contribution 0.99	0.94	0.10	asserted 0.98

What kind of paper the classifier reports this is: theoretical result 0.93 · 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 define a new notion of weak containment for joinings, and we show that this notion implies an inequality between relative Rokhlin entropies. This leads to new upper bounds to Rokhlin entropy. We also use this notion to study how Pinsker algebras behave under direct products, and we study the Rokhlin entropy of restricted actions of finite-index subgroups.

Human review

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

How the literature uses it

14 arXiv papers cite this in 31 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 · 20 sentences without a confident label

Compares with it 1 paper

Theorems [ref] and [ref] give us a Pinsker product formula for actions weakly contained in Bernoulli shift actions, and so our results are parallel to those of Seward in [ref] .

Relative entropy and the Pinsker product formula for sofic groups · Introduction · 1.00

Cites it as support 1 paper

($4 ⇐5$) This follows from Proposition [ref] and [ref] which states that the naive entropy of a generating partition is an upper bound for the Rokhlin entropy.

Zero entropy is generic · Five strengthenings of zero entropy · 0.99

Cites it as background 9 papers

This notion was inspired by Kerr's approach to sofic entropy in [ref] and has been variously called outer sofic entropy, extension entropy or entropy in the presence [ref] .

Sofic homological invariants and the Weak Pinsker Property · Questions · 0.89
Another entropy-type invariant the Rokhlin entropy was defined and investigated in works [ref] , [ref] , [ref] by Seward, and in upcoming work [ref] by Seward and myself.

Random ordering formula for sofic and Rokhlin entropy of Gibbs measures · Introduction · 1.00
This notion of entropy was studied intensively in the context of general measure-preserving group actions by Seward in the series of papers [ref] .

Shannon-McMillan-Breiman theorem along almost geodesics in negatively curved groups · Rokhlin entropy, finitary entropy and orbital entropy · 1.00

Discussion

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