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A transport process on graphs and its limiting distributions

Published online by Cambridge University Press:  10 October 2022

Leonardo Videla*
Affiliation:
Universidad de Santiago de Chile
*
*Postal address: Departamento de Matemática y Ciencia de la Computación, Universidad de Santiago de Chile, Las Sophoras 173, Estación Central, Santiago, Chile. Email address: leonardo.videla@usach.cl

Abstract

Given a finite strongly connected directed graph $G=(V, E)$ , we study a Markov chain taking values on the space of probability measures on V. The chain, motivated by biological applications in the context of stochastic population dynamics, is characterized by transitions between states that respect the structure superimposed by E: mass (probability) can only be moved between neighbors in G. We provide conditions for the ergodicity of the chain. In a simple, symmetric case, we fully characterize the invariant probability.

Type
Original Article
Copyright
© The Author(s), 2022. Published by Cambridge University Press on behalf of Applied Probability Trust

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