Stochastic domination : the contact process, Ising models and FKG measures

Thomas M. Liggett; Jeffrey E. Steif

Annales de l'I.H.P. Probabilités et statistiques (2006)

  • Volume: 42, Issue: 2, page 223-243
  • ISSN: 0246-0203

How to cite

top

Liggett, Thomas M., and Steif, Jeffrey E.. "Stochastic domination : the contact process, Ising models and FKG measures." Annales de l'I.H.P. Probabilités et statistiques 42.2 (2006): 223-243. <http://eudml.org/doc/77895>.

@article{Liggett2006,
author = {Liggett, Thomas M., Steif, Jeffrey E.},
journal = {Annales de l'I.H.P. Probabilités et statistiques},
language = {eng},
number = {2},
pages = {223-243},
publisher = {Elsevier},
title = {Stochastic domination : the contact process, Ising models and FKG measures},
url = {http://eudml.org/doc/77895},
volume = {42},
year = {2006},
}

TY - JOUR
AU - Liggett, Thomas M.
AU - Steif, Jeffrey E.
TI - Stochastic domination : the contact process, Ising models and FKG measures
JO - Annales de l'I.H.P. Probabilités et statistiques
PY - 2006
PB - Elsevier
VL - 42
IS - 2
SP - 223
EP - 243
LA - eng
UR - http://eudml.org/doc/77895
ER -

References

top
  1. [1] V. Belitsky, P. Ferrari, N. Konno, T.M. Liggett, A strong correlation inequality for contact processes and oriented percolation, Stochastic Process Appl.67 (1997) 213-225. Zbl0890.60094MR1449832
  2. [2] I. Benjamini, R. Lyons, Y. Peres, O. Schramm, Group-invariant percolation on graphs, Geom. Funct. Anal.9 (1999) 29-66. Zbl0924.43002MR1675890
  3. [3] J. van den Berg, O. Häggström, J. Kahn, Some conditional correlation inequalities for percolation and related processes, Rand. Structures Algorithms, in press. Zbl1112.60087MR2268229
  4. [4] J. Bricmont, J.L. Lebowitz, C. Maes, Percolation in strongly correlated systems: the massless Gaussian free field, J. Statist. Phys.48 (1987) 1249-1268. Zbl0962.82520MR914444
  5. [5] E.I. Broman, J.E. Steif, Dynamical stability of percolation for some interacting particle systems and ϵ-stability, Ann. Probab., in press. Zbl1107.82058
  6. [6] H.O. Georgii, Gibbs Measures and Phase Transitions, de Gruyter, 1988. Zbl0657.60122MR956646
  7. [7] O. Häggström, Infinite clusters in dependent automorphism invariant percolation on trees, Ann. Probab.25 (1997) 1423-1436. Zbl0895.60098MR1457624
  8. [8] R.A. Holley, T.M. Liggett, The survival of contact processes, Ann. Probab.6 (1978) 198-206. Zbl0375.60111MR488379
  9. [9] T.M. Liggett, Interacting Particle Systems, Springer, 1985. Zbl1103.82016MR776231
  10. [10] T.M. Liggett, Survival and coexistence in interacting particle systems, in: Probability and Phase Transition, Kluwer Academic, 1994, pp. 209-226. Zbl0832.60094MR1283183
  11. [11] T.M. Liggett, Survival of discrete time growth models, with applications to oriented percolation, Ann. Appl. Probab.5 (1995) 613-636. Zbl0842.60090MR1359822
  12. [12] T.M. Liggett, Stochastic Interacting Systems: Contact, Voter and Exclusion Processes, Springer, 1999. Zbl0949.60006MR1717346
  13. [13] T.M. Liggett, R.H. Schonmann, A.M. Stacey, Domination by product measures, Ann. Probab.25 (1997) 71-95. Zbl0882.60046MR1428500
  14. [14] R. Lyons, J.E. Steif, Stationary determinantal processes: phase multiplicity, Bernoullicity, entropy, and domination, Duke Math. J.120 (2003) 515-575. Zbl1068.82010MR2030095
  15. [15] C. Maes, F. Redig, S. Shlosman, A. van Moffaert, Percolation, path large deviations and weak Gibbsianity, Comm. Math. Phys.209 (2000) 517-545. Zbl0945.60098MR1737993
  16. [16] R.H. Schonmann, Second order large deviation estimates for ferromagnetic systems in the phase coexistence region, Comm. Math. Phys.112 (1987) 409-422. MR908546
  17. [17] C.J. Thompson, Mathematical Statistical Mechanics, Princeton University Press, 1972. Zbl0417.60096MR548873
  18. [18] J.C. Wierman, Substitution method critical probability bounds for the square lattice site percolation model, Combin. Probab. Comput.4 (1995) 181-188. Zbl0835.60089MR1342860

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.