The PDF file you selected should load here if your Web browser has a PDF reader plug-in installed (for example, a recent version of Adobe Acrobat Reader).

Alternatively, you can also download the PDF file directly to your computer, from where it can be opened using a PDF reader. To download the PDF, click the Download link below.

If you would like more information about how to print, save, and work with PDFs, Highwire Press provides a helpful Frequently Asked Questions about PDFs.

Download this PDF file Fullscreen Fullscreen Off

References

  • Aldous, D. J. and Fill, J. A. (2002). Reversible Markov Chains and Random Walks on Graphs. Available at http://www.stat.berkeley.edu/~aldous/RWG/book.html.
  • Ben Arous, Gérard; Cerf, Raphaël. Metastability of the three-dimensional Ising model on a torus at very low temperatures. Electron. J. Probab. 1 (1996), no. 10, approx. 55 pp. (electronic). MR1423463
  • Bianchi, Alessandra; Bovier, Anton; Ioffe, Dmitry. Sharp asymptotics for metastability in the random field Curie-Weiss model. Electron. J. Probab. 14 (2009), no. 53, 1541--1603. MR2525104
  • Bianchi, Alessandra; Bovier, Anton; Ioffe, Dmitry. Pointwise estimates and exponential laws in metastable systems via coupling methods. Ann. Probab. 40 (2012), no. 1, 339--371. MR2917775
  • Bobkov, Sergey G.; Tetali, Prasad. Modified logarithmic Sobolev inequalities in discrete settings. J. Theoret. Probab. 19 (2006), no. 2, 289--336. MR2283379
  • Borgs, Christian; Chayes, Jennifer T.; Tetali, Prasad. Tight bounds for mixing of the Swendsen-Wang algorithm at the Potts transition point. Probab. Theory Related Fields 152 (2012), no. 3-4, 509--557. MR2892955
  • Bovier, Anton. Metastability and ageing in stochastic dynamics. Dynamics and randomness II, 17--79, Nonlinear Phenom. Complex Systems, 10, Kluwer Acad. Publ., Dordrecht, 2004. MR2153326
  • Bovier, Anton. Metastability: a potential theoretic approach. International Congress of Mathematicians. Vol. III, 499--518, Eur. Math. Soc., Zürich, 2006. MR2275693
  • Bovier, Anton; Eckhoff, Michael; Gayrard, Véronique; Klein, Markus. Metastability and small eigenvalues in Markov chains. J. Phys. A 33 (2000), no. 46, L447--L451. MR1804034
  • Bovier, Anton; Eckhoff, Michael; Gayrard, Véronique; Klein, Markus. Metastability in stochastic dynamics of disordered mean-field models. Probab. Theory Related Fields 119 (2001), no. 1, 99--161. MR1813041
  • Bovier, Anton; Eckhoff, Michael; Gayrard, Véronique; Klein, Markus. Metastability and low lying spectra in reversible Markov chains. Comm. Math. Phys. 228 (2002), no. 2, 219--255. MR1911735
  • Bovier, Anton; Manzo, Francesco. Metastability in Glauber dynamics in the low-temperature limit: beyond exponential asymptotics. J. Statist. Phys. 107 (2002), no. 3-4, 757--779. MR1898856
  • Cassandro, Marzio; Galves, Antonio; Olivieri, Enzo; Vares, Maria Eulália. Metastable behavior of stochastic dynamics: a pathwise approach. J. Statist. Phys. 35 (1984), no. 5-6, 603--634. MR0749840
  • Cover, Thomas M.; Thomas, Joy A. Elements of information theory. Second edition. Wiley-Interscience [John Wiley & Sons], Hoboken, NJ, 2006. xxiv+748 pp. ISBN: 978-0-471-24195-9; 0-471-24195-4 MR2239987
  • Diaconis, P.; Saloff-Coste, L. Logarithmic Sobolev inequalities for finite Markov chains. Ann. Appl. Probab. 6 (1996), no. 3, 695--750. MR1410112
  • Dembo, Amir; Zeitouni, Ofer. Large deviations techniques and applications. Second edition. Applications of Mathematics (New York), 38. Springer-Verlag, New York, 1998. xvi+396 pp. ISBN: 0-387-98406-2 MR1619036
  • Hwang, Suk-Geun; Pyo, Sung-Soo. The inverse eigenvalue problem for symmetric doubly stochastic matrices. Tenth Conference of the International Linear Algebra Society. Linear Algebra Appl. 379 (2004), 77--83. MR2039298
  • Kramers, H. A. Brownian motion in a field of force and the diffusion model of chemical reactions. Physica 7, (1940). 284--304. MR0002962
  • Levin, David A.; Luczak, Malwina J.; Peres, Yuval. Glauber dynamics for the mean-field Ising model: cut-off, critical power law, and metastability. Probab. Theory Related Fields 146 (2010), no. 1-2, 223--265. MR2550363
  • Neves, E. Jordão; Schonmann, Roberto H. Critical droplets and metastability for a Glauber dynamics at very low temperatures. Comm. Math. Phys. 137 (1991), no. 2, 209--230. MR1101685
  • Neves, E. Jordão; Schonmann, Roberto H. Behavior of droplets for a class of Glauber dynamics at very low temperature. Probab. Theory Related Fields 91 (1992), no. 3-4, 331--354. MR1151800
  • Olivieri, E.; Scoppola, E. Markov chains with exponentially small transition probabilities: first exit problem from a general domain. I. The reversible case. J. Statist. Phys. 79 (1995), no. 3-4, 613--647. MR1327899
  • Thomas, Lawrence E. Bound on the mass gap for finite volume stochastic Ising models at low temperature. Comm. Math. Phys. 126 (1989), no. 1, 1--11. MR1027910
Bookmark and Share


Creative Commons License
This work is licensed under a Creative Commons Attribution 3.0 License.