Robert Grone et al 2008 J. Phys. A: Math. Theor. 41 212002 doi:10.1088/1751-8113/41/21/212002
An interlacing theorem for reversible Markov chains
FREE ARTICLERobert Grone1, Karl Heinz Hoffmann2 and Peter Salamon1
Show affiliationsFAST TRACK COMMUNICATION
Reversible Markov chains are an indispensable tool in the modeling of a vast class of physical, chemical, biological and statistical problems. Examples include the master equation descriptions of relaxing physical systems, stochastic optimization algorithms such as simulated annealing, chemical dynamics of protein folding and Markov chain Monte Carlo statistical estimation. Very often the large size of the state spaces requires the coarse graining or lumping of microstates into fewer mesoscopic states, and a question of utmost importance for the validity of the physical model is how the eigenvalues of the corresponding stochastic matrix change under this operation. In this paper we prove an interlacing theorem which gives explicit bounds on the eigenvalues of the lumped stochastic matrix.
- PACS
- MSC
-
92D20 Protein sequences, DNA sequences
- Subjects
- Dates
-
Issue 21 (30 May 2008)
Received 12 March 2008, in final form 18 April 2008
Published 7 May 2008
-
An interlacing theorem for reversible Markov chains
Robert Grone et al 2008 J. Phys. A: Math. Theor. 41 212002
-
Thermal gradient induced actuation in double-walled carbon nanotubes
Quan-Wen Hou et al 2009 Nanotechnology 20 495503
-
Resonant x-ray scattering in 3d-transition-metal oxides: Anisotropy and charge orderings
G Subías et al 2009 J. Phys.: Conf. Ser. 190 012085
-
Temperature dependence of EXAFS cumulants of Ag nanoparticles in glass
M Dubiel et al 2009 J. Phys.: Conf. Ser. 190 012123
-
Metal-Insulator Transition in CuIr2(S1−xTex)4
Yue Song et al 2009 Chinese Phys. Lett. 26 117103
-
Reduction and re-oxidation of Cu/Al2O3 catalysts investigated with quick-scanning XANES and EXAFS
J Stötzel et al 2009 J. Phys.: Conf. Ser. 190 012153
-
Evidence of kinetically arrested supercooled phases in the perovskite oxide NdNiO3
Devendra Kumar et al 2009 J. Phys.: Condens. Matter 21 485402
-
Stochastic Alternating Dynamics for Synchronous EAD-Like Beating Rhythms in Cultured Cardiac Myocytes
Zhang Ning et al 2009 Chinese Phys. Lett. 26 110501
-
Doping poly[2-methoxy-5-(2'-ethylhexyloxy)-1,4-phenylenevinylene] with PbSe nanoparticles or fullerenes
D K Chambers et al 2008 J. Phys.: Condens. Matter 20 382202
-
High-Temperature Raman Investigation on Phase Transition of LBO Crystal
Zhang Xia et al 2009 Chinese Phys. Lett. 26 113301
Users also read
What's this?- One-dimensional anyons with competing δ-function and derivative δ-function potentials
- Taming the Yukawa potential singularity: improved evaluation of bound states and resonance energies
-
Discrete
-symmetric models of scattering
-symmetric waveguideRelated review articles
What's this?- Spatiotemporal dynamics of continuum neural fields
- T-systems and Y-systems in integrable systems*
- On the uncertainty in the regularized solution