Annales Henri Poincaré

, Volume 13, Issue 6, pp 1501–1510 | Cite as

From Diffusions on Graphs to Markov Chains via Asymptotic State Lumping

  • Adam BobrowskiEmail author
Open Access


We show that fast diffusions on finite graphs with semi permeable membranes on vertices may be approximated by finite-state Markov chains provided the related permeability coefficients are appropriately small. The convergence theorem involves a singular perturbation with singularity in both operator and boundary/transmission conditions, and the related semigroups of operators converge in an irregular manner. The result is motivated by recent models of synaptic depression.


Markov Chain Line Graph Fast Diffusion Large Deviation Principle Semi Permeable Membrane 
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Open Access

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Copyright information

© The Author(s) 2012

Authors and Affiliations

  1. 1.Department of Mathematics, Faculty of Electrical Engineering and Computer ScienceLublin University of TechnologyLublinPoland

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