Student or educator? Sign up with your school email and get 6 months of Pro free.
CoChat
Sign Up
Cited by 527

The DOI matches its Crossref record; 8 of the 8 references it cites were found in a registry or an index.

Interaction of Markov Processes

Spitzer, Frank·1991·Random Walks, Brownian Motion, and Interacting Particle Systems
DOI 10.1007/978-1-4612-0459-6_5
Open this paper in CoChat — free account

Abstract

For a gentle approach to the problems connected with interacting Markov processes we review first what is known in the absence of interaction. For simplicity let S be a countable (or finite) set, and consider a countable (or finite if S is finite) collection of independent Markov processes on S,with common transition function P t (x,y), x, y ∈ S. It is natural to assume constant invariant measure, i.e., 0.1 $$ \sum\limits_{{x \in S}} {{{P}_{t}}(x,y)} = \sum\limits_{{y \in S}} {{{P}_{t}}(x,y)} = 1, x,y S, t \geqslant 0. $$

Overview

The claims and statistics of this paper haven’t been checked yet.

Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.

A few free checks a day · papers already verified open instantly · results are public

Integrity signals

Registry

Crossref · 10.1007/978-1-4612-0459-6_5

Cites

8 of 8 references verified0 citation errors · 0 not checkable

Statistics

Verification

Claims the paper makes

The claims and statistics of this paper haven’t been checked yet.

Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.

A few free checks a day · papers already verified open instantly · results are public

Self-check

Percentages, sums and reported differences re-computed from the paper’s own numbers.

The self-check needs the paper’s full text.

Citations

Cites

Show all 8 references

Cited by

See all 527

Metadata

Authors
Spitzer, F.
Venue
Random Walks, Brownian Motion, and Interacting Particle Systems
Publisher
Birkhäuser Boston
Published
1991
Pages
66-110
DOI
10.1007/978-1-4612-0459-6_5
OpenAlex
W2147301465
Cited by
527
References
8
FWCI
23.37
Type
book chapter
Language
en
Open access
closed

About these checks

Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.

Statistics and arithmetic are recomputed, not judged.

Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.

What counts as a claim ›How we measure confidence ›How we check this ›

Are you an author, or do you see a problem with this page? Request a review

How to cite

Cite CoChat for the checks on this page, and the paper for its own findings.

This page
CoChat. (2026). Citation check: Interaction of Markov Processes. https://app.cochat.ai/papers/10.1007/978-1-4612-0459-6_5
The paper
Spitzer, F. (1991). Interaction of Markov Processes. Random Walks, Brownian Motion, and Interacting Particle Systems. https://doi.org/10.1007/978-1-4612-0459-6_5

Data sources

Bibliographic data: Semantic Scholar, OpenAlex, Crossref.

Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).

Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.