Survival probabilities of high-dimensional stochastic SIS and SIR models with random edge weights

Xiaofeng Xue

RECORD

Survival probabilities of high-dimensional stochastic SIS and SIR models with random edge weights

Xiaofeng Xue

Probability · Submitted 26 Jun 2017

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

The authors' main claim Our main result gives mean field limits for survival probabilities of the two models as the dimension grows to infinity, which extends the main conclusion given in \cite{Xue2017} for classic stochastic SIS model.

how it is stated · asserted 1.00 read the record →

Comment (0) Read on arXiv ↗

Cite ▾

arXiv ID1706.08233 (version 1)

Pith IDDWKE4TZ4, Pith's permanent record of this paper and its review

CitationXiaofeng Xue. "Survival probabilities of high-dimensional stochastic SIS and SIR models with random edge weights." arXiv:1706.08233 (2017). https://pith.science/paper/DWKE4TZ4

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, 3,033 input tokens.

What the abstract itself states, as probabilities: claims first 0.06 · states limitation 0.09 · human participants 0.02 · controlled comparison 0.05 · randomized assignment 0.03 · states quantitative result 0.13 · compares with prior results 0.93 · mentions code or data availability 0.01.

The abstract, sentence by sentence

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

In this paper, we are concerned with the stochastic SIS (susceptible-infected-susceptible) and SIR (susceptible-infected-recovered) models on high-dimensional lattices with random edge weights, where a susceptible vertex is infected by an infectious neighbor at rate proportional to the weight on the edge connecting them. All the edge weights are assumed to be i.i.d.. Our main result gives mean field limits for survival probabilities of the two models as the dimension grows to infinity, which extends the main conclusion given in \cite{Xue2017} for classic stochastic SIS model.

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	In this paper, we are concerned with the stochastic SIS (susceptible-infected-susceptible) and SIR (susceptible-infected-recovered) models on high-dimensional lattices with random edge weights, where a susceptible vertex is infected by an infectious neighbor at rate proportional to the weight on the edge connecting them.	background 0.55	0.21	0.04	asserted 0.90
s1	All the edge weights are assumed to be i.i.d..	method 0.95	0.25	0.02	asserted 1.00
s2	Our main result gives mean field limits for survival probabilities of the two models as the dimension grows to infinity, which extends the main conclusion given in \cite{Xue2017} for classic stochastic SIS model.	result 0.91	0.93	0.97	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

sources read

arXiv listing abstract v1

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

In this paper, we are concerned with the stochastic SIS (susceptible-infected-susceptible) and SIR (susceptible-infected-recovered) models on high-dimensional lattices with random edge weights, where a susceptible vertex is infected by an infectious neighbor at rate proportional to the weight on the edge connecting them. All the edge weights are assumed to be i.i.d.. Our main result gives mean field limits for survival probabilities of the two models as the dimension grows to infinity, which extends the main conclusion given in \cite{Xue2017} for classic stochastic SIS model.

Human review

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

How the literature uses it

1 arXiv paper 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

Uses its method or tool 1 paper

First we give a sketch of the proof, which is inspired by the approach introduced in [ref] .

The survival probability of the high-dimensional contact process with random vertex weights on the oriented lattice · Proof of Equation [ref] · 1.00

Compares with it 1 paper

It is claimed in [ref] that [equation] for the process with edge weights which are independent copies of $ρ$ and infection rate $λ>1/Eρ$.

The survival probability of the high-dimensional contact process with random vertex weights on the oriented lattice · Main results · 0.88

What it cites · 2 sentences without a confident label

Uses the method or tool of 1 paper

The proof utilizes the following Proposition given in [ref] .

Asymptotic for critical value of the large-dimensional SIR epidemic on clusters · Proof of Lemma [ref] · 0.88

Discussion

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