Publication

Exponential Convergence for the Fredrickson-Andersen One-Spin Facilitated Model

Thomas Mountford
2019
Journal Articles

Abstract

We prove exponential convergence to equilibrium for the Fredrickson-Andersen one-spin facilitated model on bounded degree graphs satisfying a subexponential, but larger than polynomial, growth condition. This was a classical conjecture related to non-attractive spin systems. Our proof relies on coupling techniques based on Harris graphical construction for interacting particle systems.

Official source

https://infoscience.epfl.ch/entities/publication/a4f3fa9d-fcac-4f61-97f8-e76bebc710bc

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Thomas Mountford
2019
Journal Articles

Abstract

Official source

https://infoscience.epfl.ch/entities/publication/a4f3fa9d-fcac-4f61-97f8-e76bebc710bc

About this result

Related concepts (13)

Expander graph

In graph theory, an expander graph is a sparse graph that has strong connectivity properties, quantified using vertex, edge or spectral expansion. Expander constructions have spawned research in pure and applied mathematics, with several applications to complexity theory, design of robust computer networks, and the theory of error-correcting codes. Intuitively, an expander graph is a finite, undirected multigraph in which every subset of the vertices that is not "too large" has a "large" boundary.

Bipartite graph

In the mathematical field of graph theory, a bipartite graph (or bigraph) is a graph whose vertices can be divided into two disjoint and independent sets and , that is, every edge connects a vertex in to one in . Vertex sets and are usually called the parts of the graph. Equivalently, a bipartite graph is a graph that does not contain any odd-length cycles. The two sets and may be thought of as a coloring of the graph with two colors: if one colors all nodes in blue, and all nodes in red, each edge has endpoints of differing colors, as is required in the graph coloring problem.

Perfect graph

In graph theory, a perfect graph is a graph in which the chromatic number equals the size of the maximum clique, both in the graph itself and in every induced subgraph. In all graphs, the chromatic number is greater than or equal to the size of the maximum clique, but they can be far apart. A graph is perfect when these numbers are equal, and remain equal after the deletion of arbitrary subsets of vertices. The perfect graphs include many important families of graphs and serve to unify results relating colorings and cliques in those families.

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Random walks and forbidden minors III: poly(d epsilon(-1))-time partition oracles for minor-free graph classes

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Consider the family of bounded degree graphs in any minor-closed family (such as planar graphs). Let d be the degree bound and n be the number of vertices of such a graph. Graphs in these classes have hyperfinite decompositions, where, one removes a small ...

IEEE COMPUTER SOC2022