Result: From Diffusions on Graphs to Markov Chains via Asymptotic State Lumping
Title:
From Diffusions on Graphs to Markov Chains via Asymptotic State Lumping
Authors:
Source:
Annales Henri Poincaré. 13(6):1501-1510
Publisher Information:
Heidelberg: Springer, 2012.
Publication Year:
2012
Physical Description:
print, 34 ref
Original Material:
INIST-CNRS
Subject Terms:
Mathematics, Mathématiques, Physics, Physique, Theoretical physics, Physique théorique, Sciences exactes et technologie, Exact sciences and technology, Sciences et techniques communes, Sciences and techniques of general use, Mathematiques, Mathematics, Probabilités et statistiques, Probability and statistics, Théorie des probabilités et processus stochastiques, Probability theory and stochastic processes, Processus de markov, Markov processes, Analyse numérique. Calcul scientifique, Numerical analysis. Scientific computation, Analyse numérique, Numerical analysis, Probabilités et statistiques numériques, Numerical methods in probability and statistics, Physique, Physics, Generalites, General, Méthodes mathématiques en physique, Mathematical methods in physics, Divers, Other topics in mathematical methods in physics, Chaîne Markov, Markov chain, Cadena Markov, Chaîne graphe, Graph chain, Cadena grafo, Condition aux limites, Boundary conditions, Diffusion, Scattering, Dépression synaptique, Synaptic depression, Depresión sináptica, Graphe fini, Finite graph, Grafo finito, Membrane, Membranes, Perméabilité, Permeability, Perturbation singulière, Singular perturbation, Perturbación singular, Physique mathématique, Mathematical physics, Semigroupe opérateur, Operator semigroup, Semigrupo operador, Singularité, Singularity, Transmission, 60J10, 65C40, Théorème convergence
Document Type:
Academic journal
Article
File Description:
text
Language:
English
Author Affiliations:
Department of Mathematics Faculty of Electrical Engineering and Computer Science Lublin University of Technology Nadbystrzycka 38A, 20-618 Lublin, Poland
ISSN:
1424-0637
Rights:
Copyright 2015 INIST-CNRS
CC BY 4.0
Sauf mention contraire ci-dessus, le contenu de cette notice bibliographique peut être utilisé dans le cadre d’une licence CC BY 4.0 Inist-CNRS / Unless otherwise stated above, the content of this bibliographic record may be used under a CC BY 4.0 licence by Inist-CNRS / A menos que se haya señalado antes, el contenido de este registro bibliográfico puede ser utilizado al amparo de una licencia CC BY 4.0 Inist-CNRS
CC BY 4.0
Sauf mention contraire ci-dessus, le contenu de cette notice bibliographique peut être utilisé dans le cadre d’une licence CC BY 4.0 Inist-CNRS / Unless otherwise stated above, the content of this bibliographic record may be used under a CC BY 4.0 licence by Inist-CNRS / A menos que se haya señalado antes, el contenido de este registro bibliográfico puede ser utilizado al amparo de una licencia CC BY 4.0 Inist-CNRS
Notes:
Mathematics
Theoretical physics
Theoretical physics
Accession Number:
edscal.26256337
Database:
PASCAL Archive
Further Information
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.