Fast Mixing for the Low Temperature 2D Ising Model Through Irreversible Parallel Dynamics

详细信息    查看全文

• 作者：Paolo Dai Pra (1)
  Benedetto Scoppola (2)
  Elisabetta Scoppola (3)
  
  1. Dipartimento di Matematica ; University of Padova ; Via Trieste 63 ; 35121 ; Padua ; Italy
  2. Dipartimento di Matematica ; University of Roma 鈥淭or Vergata鈥? Via della Ricerca Scientifica ; 00133 ; Roma ; Italy
  3. Dipartimento di Matematica e Fisica ; University of Roma 鈥淩oma Tre鈥? Largo San Murialdo ; 1 ; 00146 ; Roma ; Italy
  
• 关键词：Tunneling ; Mixing times ; Probabilistic cellular automata
• 刊名：Journal of Statistical Physics
• 出版年：2015
• 出版时间：April 2015
• 年：2015
• 卷：159
• 期：1
• 页码：1-20
• 全文大小：235 KB
• 参考文献：1. Anderson, BDO, Kailath, T (1979) Forwards, backwards and dynamically reversible Markovian models of second-order processes. IEEE Trans. Circuits Syst. 26: pp. 956-965 CrossRef
  2. Beltran, J, Landim, C (2010) Tunneling and metastability of continuous time Markov chains. J. Stat. Phys. 140: pp. 1065-1114 CrossRef
  3. Pra, P, Scoppola, B (2012) Scoppola sampling from a Gibbs measure with pair interaction by means of PCA. J. Stat. Phys. 149: pp. 722-737 CrossRef
  4. Feller, W (1968) An Introduction to Probability Theory and Its Applications. Wiley, New York
  5. Jerrum, M., Sinclair, A.: The Markov Chain Monte Carlo method: an approach to approximate counting and integration. In: Approximation algorithms for NP-hard problems, pp. 482鈥?20. PWS Publishing Co., Boston, MA (1996)
  6. Lancia, C, Scoppola, B (2013) Equilibrium and non-equilibrium Ising models by means of PCA. J. Stat. Phys. 154: pp. 641-653 CrossRef
  7. Martinelli, F Relaxation times of Markov chains in statistical mechanics and combinatorial structures. In: Sznitman, AS, Varadhan, SRS eds. (2004) Probability on Discrete Structures. Springer, New York CrossRef
  8. Martinelli, F (1992) Dynamical analysis of low-temperature Monte Carlo cluster algorithms. J. Stat. Phys. 66: pp. 1245-1276 CrossRef
  9. Olivieri, E, Vares, ME (2005) Large Deviations and Metastability. Cambridge University Press, Cambridge CrossRef
  10. Scoppola, E (1993) Renormalization group for Markov chains and application to metastability. J. Stat. Phys. 73: pp. 83-121 CrossRef
  11. Toom, A (1980) Stable and attractive trajectories in multicomponent systems. Adv. Probab. 6: pp. 549-575
  
• 刊物类别：Physics and Astronomy
• 刊物主题：Physics
  Statistical Physics
  Mathematical and Computational Physics
  Physical Chemistry
  Quantum Physics
  
• 出版者：Springer Netherlands
• ISSN：1572-9613

文摘

We study tunneling and mixing time for a non-reversible probabilistic cellular automaton. With a suitable choice of the parameters, we first show that the stationary distribution is close in total variation to a low temperature Ising model. Then we prove that both the mixing time and the time to exit a metastable state grow polynomially in the size of the system, while this growth is exponential in reversible dynamics. In this model, non-reversibility, parallel updatings and a suitable choice of boundary conditions combine to produce an efficient dynamical stability.