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Volumn 41, Issue 3, 2000, Pages 1598-1615

Analyzing Glauber dynamics by comparison of Markov chains

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EID: 0034345469     PISSN: 00222488     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.533199     Document Type: Review
Times cited : (100)

References (38)
  • 1
    • 0000002644 scopus 로고    scopus 로고
    • Mathematical foundations of the Markov Chain Monte Carlo method
    • edited by Habib et al. Springer-Verlag, New York
    • M. Jerrum, "Mathematical Foundations of the Markov Chain Monte Carlo Method," in Probabilistic Methods for Algorithmic Discrete Mathematics, edited by Habib et al. (Springer-Verlag, New York, 1998), pp. 116-165.
    • (1998) Probabilistic Methods for Algorithmic Discrete Mathematics , pp. 116-165
    • Jerrum, M.1
  • 3
    • 0002044942 scopus 로고    scopus 로고
    • Approximate counting
    • edited by R. A. Bailey (Cambridge U. P. Cambridge, 1997); London Math Society Lecture Notes
    • D. J. A. Welsh, "Approximate counting," in Surveys in Combinatorics, edited by R. A. Bailey (Cambridge U. P. Cambridge, 1997); London Math Society Lecture Notes 241, 287-317 (1997).
    • (1997) Surveys in Combinatorics , vol.241 , pp. 287-317
    • Welsh, D.J.A.1
  • 4
    • 0024699930 scopus 로고
    • Approximate counting, uniform generation and rapidly mixing Markov chains
    • A. J. Sinclair and M. R. Jerrum, "Approximate counting, uniform generation and rapidly mixing Markov chains," Information and Computation 82, 93-133 (1989).
    • (1989) Information and Computation , vol.82 , pp. 93-133
    • Sinclair, A.J.1    Jerrum, M.R.2
  • 5
    • 0024904712 scopus 로고
    • Approximating the permanent
    • M. R. Jerrum and A. J. Sinclair, "Approximating the permanent," SIAM J. Comput. 18, 1149-1178 (1989).
    • (1989) SIAM J. Comput. , vol.18 , pp. 1149-1178
    • Jerrum, M.R.1    Sinclair, A.J.2
  • 6
    • 0038971757 scopus 로고    scopus 로고
    • Approximating the number of dimer coverings of a lattice
    • C. Kenyon, D. Randall, and A. Sinclair, "Approximating the number of dimer coverings of a lattice," Stat. Phys. 83, 637-659 (1996).
    • (1996) Stat. Phys. , vol.83 , pp. 637-659
    • Kenyon, C.1    Randall, D.2    Sinclair, A.3
  • 7
    • 0027677367 scopus 로고
    • Polynomial-time approximation algorithms for the Ising model
    • M. R. Jerrum and A. J. Sinclair, "Polynomial-time approximation algorithms for the Ising model," SIAM J. Comput. 22, 1087-1116 (1993).
    • (1993) SIAM J. Comput. , vol.22 , pp. 1087-1116
    • Jerrum, M.R.1    Sinclair, A.J.2
  • 8
    • 0000569649 scopus 로고
    • Random walks on finite groups and rapidly mixing Markov chains
    • Springer Lecture Notes in Mathematics
    • D. Aldous, "Random walks on finite groups and rapidly mixing Markov chains," in Séminaire de Probabilités XVII, 1981/82, Springer Lecture Notes in Mathematics, Vol. 986, pp. 243-297.
    • (1981) Séminaire de Probabilités XVII , vol.986 , pp. 243-297
    • Aldous, D.1
  • 9
    • 84990721683 scopus 로고
    • A very simple algorithm for estimating the number of k-colorings of a low-degree graph
    • M. Jerrum, "A very simple algorithm for estimating the number of k-colorings of a low-degree graph," Random Structures and Algorithms 7, 157-165 (1995).
    • (1995) Random Structures and Algorithms , vol.7 , pp. 157-165
    • Jerrum, M.1
  • 15
    • 33645652905 scopus 로고    scopus 로고
    • On the mixing time of the triangulation walk and other Catalan structures
    • DIMACS-AMS
    • L. McShine and P. Tetali, "On the mixing time of the triangulation walk and other Catalan structures," Randomization Methods in Algorithm Design, DIMACS-AMS Vol. 43 (1998), pp. 147-160.
    • (1998) Randomization Methods in Algorithm Design , vol.43 , pp. 147-160
    • McShine, L.1    Tetali, P.2
  • 16
    • 85037769932 scopus 로고    scopus 로고
    • On Markov chains for independent sets
    • to appear
    • M. Dyer and C. Greenhill, "On Markov chains for independent sets," J. of Algorithms (to appear).
    • J. of Algorithms
    • Dyer, M.1    Greenhill, C.2
  • 17
    • 84949224014 scopus 로고    scopus 로고
    • Analyzing Glauber dynamics by comparisons of Markov chains
    • Springer Lecture Notes in Computer Science
    • D. Randall and P. Tetali, "Analyzing Glauber dynamics by comparisons of Markov chains," Proceedings 3rd Latin American Theoretical Informatics Symposium, Springer Lecture Notes in Computer Science (1998), Vol. 1380, pp. 292-304.
    • (1998) Proceedings 3rd Latin American Theoretical Informatics Symposium , vol.1380 , pp. 292-304
    • Randall, D.1    Tetali, P.2
  • 18
    • 0000255332 scopus 로고
    • Comparison theorems for reversible Markov chains
    • P. Diaconis and L. Saloff-Coste, "Comparison theorems for reversible Markov chains," Ann. Appl. Probability 3, 696-730 (1993).
    • (1993) Ann. Appl. Probability , vol.3 , pp. 696-730
    • Diaconis, P.1    Saloff-Coste, L.2
  • 19
    • 0002740591 scopus 로고
    • Geometric bounds for eigenvalues of Markov chains
    • P. Diaconis and D. Stroock, "Geometric bounds for eigenvalues of Markov chains," Ann. Appl. Probability 1, 36-61 (1991).
    • (1991) Ann. Appl. Probability , vol.1 , pp. 36-61
    • Diaconis, P.1    Stroock, D.2
  • 21
    • 0030487036 scopus 로고    scopus 로고
    • Logarithmic Sobolev inequalities for finite Markov chains
    • P. Diaconis and L. Saloff-Coste, "Logarithmic Sobolev inequalities for finite Markov chains," Ann. Appl. Probab. 6, 695-750 (1996).
    • (1996) Ann. Appl. Probab. , vol.6 , pp. 695-750
    • Diaconis, P.1    Saloff-Coste, L.2
  • 23
    • 0034345466 scopus 로고    scopus 로고
    • Random sampling for the monomer-dimer model on a lattice
    • J. van den Berg and R. Brouwer, "Random sampling for the monomer-dimer model on a lattice," J. Math. Phys. 41, 1585-1597 (2000).
    • (2000) J. Math. Phys. , vol.41 , pp. 1585-1597
    • Van Den Berg, J.1    Brouwer, R.2
  • 28
    • 0000821829 scopus 로고
    • Conway's tiling group
    • W. Thurston, "Conway's tiling group," Am. Math. Monthly 97, 757-773 (1990).
    • (1990) Am. Math. Monthly , vol.97 , pp. 757-773
    • Thurston, W.1
  • 30
    • 84968502341 scopus 로고
    • Rotation distance, triangulations, and hyperbolic geometry
    • D. Sleator, R. Tarjan, and W. Thurston, "Rotation distance, triangulations, and hyperbolic geometry," J. Am. Math. Soc. 1, (1988).
    • (1988) J. Am. Math. Soc. , vol.1
    • Sleator, D.1    Tarjan, R.2    Thurston, W.3
  • 33
    • 49149134596 scopus 로고
    • The basic contact processes
    • D. Griffeath, "The basic contact processes," Stochastic Proc. Appl 11, 151-185 (1981).
    • (1981) Stochastic Proc. Appl , vol.11 , pp. 151-185
    • Griffeath, D.1
  • 34
    • 0000858580 scopus 로고    scopus 로고
    • Lectures on finite Markov chains
    • L. Saloff-Coste, "Lectures on finite Markov chains," Lecture Notes in Math. 1665, 301-413 (1997).
    • (1997) Lecture Notes in Math. , vol.1665 , pp. 301-413
    • Saloff-Coste, L.1
  • 37
    • 0001076208 scopus 로고
    • Comparison techniques for random walks on finite groups
    • P. Diaconis and L. Saloff-Coste, "Comparison techniques for random walks on finite groups," Ann. Prob. 21, 2131-2156 (1993).
    • (1993) Ann. Prob. , vol.21 , pp. 2131-2156
    • Diaconis, P.1    Saloff-Coste, L.2
  • 38
    • 0033436481 scopus 로고    scopus 로고
    • Fast convergence of the Glauber dynamics for sampling independent sets
    • M. Luby and E. Vigoda, "Fast convergence of the Glauber dynamics for sampling independent sets," Random Structures and Algorithms 15, 229-241 (1999).
    • (1999) Random Structures and Algorithms , vol.15 , pp. 229-241
    • Luby, M.1    Vigoda, E.2


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