Work

Invariant monotone coupling need not exist

Year: 2013

Type: article

Abstract: We show by example that there is a Cayley graph, having two invariant random subgraphs $X$ and $Y$, such that there exists a monotone coupling between them in the sense that $X\subset Y$, although no such coupling can be invariant. Here, “invariant” means that the distribution is invariant under group multiplications.

Source: The Annals of Probability

DOI: 10.1214/12-aop767

Author: Péter Mester

Institution: Indiana University

Language: English

Topic: Stochastic processes and statistical mechanics

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: bronze

Funders: National Science Foundation, Hungarian Scientific Research Fund

Awards: G1871396287, Probability on Combinatorial Structures, Probability and Discrete Structures