N Destainville 2003 J. Phys. A: Math. Gen. 36 3647 doi:10.1088/0305-4470/36/13/301
N Destainville
Show affiliationsWe propose an exact technique to calculate lower bounds of spectral gaps of discrete time reversible Markov chains on finite state sets. Spectral gaps are a common tool for evaluating convergence rates of Markov chains. As an illustration, we successfully use this technique to evaluate the 'absorption time' of the 'Backgammon model', a paradigmatic model for glassy dynamics. We also discuss the application of this technique to the 'contingency table problem', a notoriously difficult problem from probability theory. The interest of this technique is that it connects spectral gaps, which are quantities related to dynamics, with static quantities, calculated at equilibrium.
05.40.-a Fluctuation phenomena, random processes, noise, and Brownian motion
60J22 Computational methods in Markov chains (See also 65C40)
82B80 Numerical methods (Monte Carlo, series resummation, etc.) (See also 65-XX, 81T80)
Issue 13 (4 April 2003)
Received 15 November 2002, in final form 6 February 2003
Published 19 March 2003
N Destainville 2003 J. Phys. A: Math. Gen. 36 3647
R. Fitzpatrick et al 1993 Nucl. Fusion 33 1533
C P Burgess 2007 Class. Quantum Grav. 24 S795
Pascal Hannequin and Jacky Mas 2002 Phys. Med. Biol. 47 4329
Man Hoi Lee 2001 J. Phys. A: Math. Gen. 34 10219
Saburo Nasu et al 2002 J. Phys.: Condens. Matter 14 11167
Anil Shaji 2004 J. Phys. A: Math. Gen. 37 11285
Elizabeth A Ainsbury et al 2005 Phys. Med. Biol. 50 3197
M Lachièze-Rey 2004 J. Phys. A: Math. Gen. 37 5625
E K Loginov 2004 J. Phys. A: Math. Gen. 37 6599