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2 results on '"15B51, 40A20, 52C25, 60J05"'

1. Triangulated Laman Graphs, Local Stochastic Matrices, and Limits of Their Products

Author

Belabbas, Mohamed Ali and Chen, Xudong

Subjects
Mathematics - Optimization and Control, Mathematics - Probability, 15B51, 40A20, 52C25, 60J05
Abstract

We derive conditions on the products of stochastic matrices guaranteeing the existence of a unique limit invariant distribution. Belying our approach is the hereby defined notion of restricted triangulated Laman graphs. The main idea is the following: to each triangle in the graph, we assign a stochastic matrix. Two matrices can be adjacent in a product only if their corresponding triangles share an edge in the graph. We provide an explicit formula for the limit invariant distribution of the product in terms of the individual stochastic matrices.

Published
2020

2. Triangulated Laman graphs, local stochastic matrices, and limits of their products

Author

Mohamed-Ali Belabbas and Xudong Chen

Subjects
Numerical Analysis, Algebra and Number Theory, Distribution (number theory), Probability (math.PR), 010102 general mathematics, MathematicsofComputing_NUMERICALANALYSIS, Stochastic matrix, 010103 numerical & computational mathematics, 15B51, 40A20, 52C25, 60J05, 01 natural sciences, Combinatorics, Optimization and Control (math.OC), Product (mathematics), Laman graph, FOS: Mathematics, Discrete Mathematics and Combinatorics, Graph (abstract data type), Geometry and Topology, Limit (mathematics), 0101 mathematics, Invariant (mathematics), Mathematics - Optimization and Control, Mathematics - Probability, MathematicsofComputing_DISCRETEMATHEMATICS, Mathematics
Abstract

We derive conditions on the products of stochastic matrices guaranteeing the existence of a unique limit invariant distribution. Belying our approach is the hereby defined notion of restricted triangulated Laman graphs. The main idea is the following: to each triangle in the graph, we assign a stochastic matrix. Two matrices can be adjacent in a product only if their corresponding triangles share an edge in the graph. We provide an explicit formula for the limit invariant distribution of the product in terms of the individual stochastic matrices.

Published
2021

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